Circles

CBSE Class 10 Mathematics · 136 board questions from this chapter; 132 listed below, 2022–2026

• In the given figure, PQ and PR are tangents to a circle with centre O and radius 3 cm. If ∠ QPR=60^°, then the length of each…2026
• In the given figure, PQ is tangent to the circle with centre O. S is a point on the circle such that ∠ SQT=55^°. The m ∠ QPS is2026
• If PQ and PR are tangents to the circle with centre O and radius 4 cm such that ∠ QPR=90^°, then the length OP is2026
• PQ is tangent to a circle with centre O. If OQ=a, OP=a+2 and PQ=2 b, then relation between a and b is2026
• From an external point P, a tangent PT has been drawn to a circle with centre at O and radius 3 cm, intersecting its concentric…2026
• If TP and TQ are two tangents to a circle with centre O from an external point T so that ∠ POQ=120^°, then ∠ PTQ is equal to:2026
• In the given figure, PT is a tangent to the circle with centre O and radius r. If ∠ POT=45^°, then the length of OP is:2026
• In the given figure, PA and PB are tangents to a circle centred at O. If ∠ OAB=15^°, then ∠ APB equals:2026
• In the given figure, PA is a tangent from an external point P to a circle with centre O. If ∠ POB=125^°, then ∠ APO is equal to:2026
• PQ is tangent to a circle with centre O. If ∠ POR=65^°, then m ∠ PTR is2026
• PA and PB are tangents to a circle centred at O. If ∠ PBA=65^°, then ∠ APB equals:2026
• In the given figure, PA is a tangent from an external point P to a circle with centre O. If ∠ POB=125^°, then ∠ APO is equal to:2026
• In the given figure, PA and PB are tangents to a circle centred at O. If ∠ AOB=130^°, then ∠ APB is equal to:2026
• Assertion: Radius is the smallest distance of a tangent from the centre of the circle. Reason (R): Radius is perpendicular to the…2026
• In the given figure, a circle with centre O is inscribed inside Δ LMN. A and B are the points of tangency. Find ∠ ANB.2026
• Two concentric circles are of radii 5 cm and 4 cm. Find the length of the chord of the larger circle which touches the smaller…2026
• In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic.2026
• Chord AB of a circle with centre O and radius 21 mm subtends an angle of 120^o at the centre. Find the perimeters of the shaded…2026
• In the given figure, Δ ABC is a right triangle in which ∠ B=90^°, AB=4 cm and BC=3 cm. Find the radius of the circle inscribed in…2026
• Prove that the lengths of tangents drawn from an external point to a circle are equal. OR Two tangents TP and TQ are drawn to a…2026
• In the given figure, ABC is a right triangle in which ∠ B=90^°, AB=4 cm and BC=3 cm. Find the radius of the circle inscribed in…2026
• Chord AB subtends an angle of 120° at the centre O of the circle with radius 21/2 cm. Find the perimeter of shaded segment ACB.…2026
• Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. OR If a regular…2026
• In the given figure, TP and TQ are tangents to a circle with centre M, touching another circle with centre N at A and B…2026
• PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP.…2026
• In the adjoining figure, AP and AQ are tangents to the circle with centre O. If reflex ∠ POQ=210^°, the value of 2 x is2025
• In the adjoining figure, AC is diameter of larger circle with centre O. AB is tangent to smaller circle with centre O. If OD=r,…2025
• The tangents drawn at the extremities of the diameter of a circle are always:2025
• In the given figure, RS is the tangent to the circle at the point L and MN is the diameter. If ∠ NML=30^°, then ∠ RLM is:2025
• If tangents PA and PB drawn from an external point P to the circle with centre O are inclined to each other at an angle of 80° as…2025
• In the adjoining figure, PA and PB are tangents to a circle with centre O such that ∠ P=90^°. If AB=3 √2 cm, then the diameter of…2025
• Which of the following statements is false?2025
• For a circle with centre O and radius 5 cm, which of the following statements is true? P: Distance between every pair of parallel…2025
• In the adjoining figure, PA and PB are tangents to a circle with centre O. The measure of angle APB is2025
• In the adjoining figure, TS is a tangent to a circle with centre O. The value of 2 x^° is2025
• If the length of a chord of a circle is equal to its radius, then the angle subtended by chord at the centre is:2025
• In the adjoining figure, AB is the chord of the larger circle touching the smaller circle. The centre of both the circles is O.…2025
• In the adjoining figure, AB is the chord of larger circle which touches the smaller circle at P. If length of AB= diameter of…2025
• In the adjoining figure, the sum of radii of two concentric circles is 16 cm. The length of chord A B which touches the inner…2025
• A parallelogram having one of its sides 5 cm circumscribes a circle. The perimeter of parallelogram is:2025
• In the given figure, PA is a tangent from an external point P to a circle with centre O. If ∠ POB=115^°, then ∠ APO is equal to:2025
• Assertion: A line drawn perpendicular to the tangent at point of contact passes through the centre of the circle. Reason (R):…2025
• Assertion: Tangents drawn at the end points of a diameter of a circle are always parallel to each other. Reason (R): The lengths…2025
• Assertion: If two tangents are drawn to a circle from an external point, then they subtend equal angles at the centre of the…2025
• The coordinates of the centre of a circle are (2a, a - 7). Find the value(s) of 'a' if the circle passes through the point (11,…2025
• At point A on the diameter AB of a circle of radius 10 cm, tangent XAY is drawn to the circle. Find the length of the chord CD…2025
• A person is standing at P outside a circular ground at a distance of 26 m from the centre of the ground. He found that his…2025
• Prove that the tangents drawn at the ends of a diameter of a circle are parallel.2025
• In the given figure, O is the centre of the circle and BCD is tangent to it at C. Prove that ∠ BAC+∠ ACD=90^°. OR Prove that…2025
• Prove that the parallelogram circumscribing a circle is a rhombus. OR Prove that the angle between the two tangents drawn from an…2025
• In the given figure, PB is a tangent to the circle with centre O at B. AB is a chord of the circle of length 24 cm and at a…2025
• In the adjoining figure, XY and X'Y' are parallel tangents to a circle with centre O. Another tangent AB touches the circle at C…2025
• In the given figure, PC is a tangent to the circle at C. AOB is the diameter which when extended meets the tangent at P. Find ∠…2025
• Rectangle ABCD circumscribes the circle of radius 10 cm. Prove that ABCD is a square. Hence, find the perimeter of ABCD.2025
• In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If ∠ OPQ=15^° and ∠ PTQ=θ, then find the value…2025
• There is a circular park of diameter 65 m as shown in the following figure, where AB is a diameter. An entry gate is to be…2025
• In the given figure, PT is tangent to a circle with centre O. Chord PQ subtends an angle of 65° at the centre. The measure of ∠…2024
• The area of the square inscribed in a circle of radius 5 √2 cm is:2024
• Maximum number of common tangents that can be drawn to two circles intersecting at two distinct points is:2024
• In the given figure, if PT is a tangent to a circle with centre O and ∠ TPO=35^°, then the measure of ∠ x is:2024
• A chord of a circle of radius 10 cm subtends a right angle at its centre. The length of the chord (in cm) is:2024
• In the given figure, tangents PA and PB to the circle centred at O, from point P are perpendicular to each other. If PA=5 cm,…2024
• In the given figure, AB and AC are tangents to the circle. If ∠ ABC=42^°, then the measure of ∠ BAC is:2024
• In the given figure, RJ and RL are two tangents to the circle. If ∠ RJL=42^°, then the measure of ∠ JOL is:2024
• In the given figure, AT is tangent to a circle centred at O. If ∠ CAT=40^°, then ∠ CBA is equal to2024
• In the given figure, O is the centre of the circle. MN is the chord and the tangent ML at point M makes an angle of 70^° with MN.…2024
• In the given figure, QR is a common tangent to the two given circles touching externally at A. The tangent at A meets QR at P. If…2024
• Assertion: The tangents drawn at the end points of a diameter of a circle, are parallel. Reason (R): Diameter of a circle is the…2024
• In the given figure, Δ ABC is circumscribing a circle. Find the length of BC, if AR=4 cm, BR=3 cm and AC=11 cm.2024
• If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm, then find the length of each tangent. OR Prove…2024
• In the given figure, AB and CD are tangents to a circle centred at O. Is ∠ BAC=∠ DCA? Justify your answer.2024
• In the given figure, O is the centre of the circle. If ∠ AOB=145^°, then find the value of x.2024
• In the given figure, PQ is tangent to a circle centred at O and ∠ BAQ=30^°; show that BP=BQ. OR In the given figure, AB, BC, CD…2024
• Prove that the parallelogram circumscribing a circle is a rhombus.2024
• Prove that the tangents drawn at the end points of a chord of a circle makes equal angles with the chord.2024
• From an external point P, two tangents PA and PB are drawn to the circle with centre O. Prove that OP is the perpendicular…2024
• In the given figure, AB is a diameter of the circle with centre O. AQ, BP and PQ are tangents to the circle. Prove that ∠…2024
• Prove that the parallelogram circumscribing a circle is a rhombus.2024
• Prove that the tangents drawn at the end points of a chord of a circle makes equal angles with the chord.2024
• A backyard is in the shape of a triangle ABC with right angle at B. AB=7 m and BC=15 m. A circular pit was dug inside it such…2024
• In the given figure, TA is a tangent to the circle with centre O such that OT=4 cm, ∠ OTA=30^°, then length of TA is:2023
• In the given figure, PQ is tangent to the circle centred at O. If ∠ AOB=95^°, then the measure of ∠ ABQ will be2023
• PQ is tangent to a circle centered at O. If the radius of the circle is 5 cm, then the length of the tangent PQ is:2023
• In the given figure, AB=BC=10 cm. If AC=7 cm, then the length of BP is:2023
• In the given figure, AB is a tangent to the circle centered at O. If OA=6 cm and ∠ OAB=30^°, then the radius of the circle is:2023
• The length of tangent drawn to a circle of radius 9 cm from a point 41 cm from the centre is:2023
• In the given figure, O is the centre of the circle and PQ is the chord. If the tangent PR at P makes an angle of 50^° with PQ,…2023
• In the given figure, PA and PB are tangents from external point P to a circle with centre C and Q is any point on the circle.…2023
• In the given figure, PQ is a tangent to the circle with centre O. If ∠ OPQ=x, ∠ POQ=y, then x+y is:2023
• In the given figure, TA is a tangent to the circle with centre O such that OT=4 cm, ∠ OTA=30^°, then length of TA is:2023
• In the given figure, the quadrilateral PQRS circumscribes a circle. Here PA+CS is equal to:2023
• In the given figure, PT is a tangent at T to the circle with centre O. If ∠ TPO=25^°, then x is equal to:2023
• In the given figure, AC and AB are tangents to a circle centered at O. If ∠ COD=120^°, then ∠ BAO is equal to:2023
• In the given figure, AB ∥ PQ. If AB=6 cm, PQ=2 cm and OB=3 cm, then the length of OP is:2023
• Assertion: A tangent to a circle is perpendicular to the radius through the point of contact. Reason (R): The lengths of tangents…2023
• Assertion: If the points A(4, 3) and B(x, 5) lie on a circle with centre O(2,3), then the value of x is 2. Reason (R): Centre of…2023
• Assertion: If PA and PB are tangents drawn from an external point P to a circle with centre O, then the quadrilateral AOBP is…2023
• In the given figure, PT is a tangent to the circle centered at O. OC is perpendicular to chord AB. Prove that PA. PB=PC^2-AC^2.2023
• In the given figure, O is the centre of the circle. AB and AC are tangents drawn to the circle from point A. If ∠ BAC=65^°, then…2023
• Prove that the tangents drawn at the ends of a diameter of a circle are parallel.2023
• In the given figure, PA is a tangent to the circle drawn from the external point P and PBC is the secant to the circle with BC as…2023
• In the given figure, O is the centre of the circle. AB and AC are tangents drawn to the circle from point A. If ∠ BAC=65^°, then…2023
• In the given figure, PQ is a chord of the circle centered at O. PT is a tangent to the circle at P. If ∠ QPT=55^°, then find ∠…2023
• The centre of a circle is (2a, a -7). Find the values of 'a' if the circle passes through the point (11, -9). Radius of the…2023
• From an external point, two tangents are drawn to a circle. Prove that the line joining the external point to the centre of the…2023
• Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by…2023
• Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠ PTQ=2 ∠ OPQ. OR In the given…2023
• Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller…2023
• In the given figure, O is the centre of the circle and QPR is a tangent to it at P. Prove that ∠ QAP+∠ APR=90^°.2023
• Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠ PTQ=2 ∠ OPQ. OR A circle…2023
• A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 10 cm and 8 cm…2023
• Prove that a parallelogram circumscribing a circle is a rhombus. OR In the given figure, tangents PQ and PR are drawn to a circle…2023
• The discus throw is an event in which an athlete attempts to throw a discus. The athlete spins anti-clockwise around one and a…2023
• The discus throw is an event in which an athlete attempts to throw a discus. The athlete spins anti-clockwise around one and a…2023
• In Figure 1, PQ and PR are tangents to the circle centred at O. If ∠ OPR=45^°, then prove that ORPQ is a square. Figure 12022
• In Fig. 1, AB is diameter of a circle centered at O. BC is tangent to the circle at B. If OP bisects the chord AD and ∠ AOP=60^°,…2022
• In Fig. 1, AB is diameter of a circle centered at O. BC is tangent to the circle at B. If OP bisects the chord AD and ∠ AOP=60^°,…2022
• Two concentric circles are of radii 4 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller…2022
• In Figure 2, PQ and PR are tangents to the circle centred at O. If ∠ OPR=45^°, then prove that ORPQ is a square. Figure 22022
• Construct a pair of tangents to a circle of radius 4 cm which are inclined to each other at an angle of 60°.2022
• Construct a pair of tangents to a circle of radius 4 cm from a point P lying outside the circle at a distance of 6 cm from the…2022
• Construct a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.2022
• Construct a pair of tangents to a circle of radius 3 cm which are inclined to each other at an angle of 60°.2022
• Construct a pair of tangents to a circle of radius 5 cm, which are inclined to each other at an angle of 60°.2022
• In Figure 1, a right triangle ABC in which ∠ B=90^°, AB=12 cm and BC=5 cm is shown. Find the radius of the circle inscribed in…2022
• In Fig.-2, if a circle touches the side QR of PQR at S and extended sides PQ and PR at M and N, respectively, then Fig. 2 prove…2022
• In Figure 3, two circles with centres at O and O' of radii 2r and r respectively, touch each other internally at A. A chord AB of…2022
• In Fig. 4, PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q meet at a point T. Find the length of…2022
• In Figure 3, two circles with centres at O and O^′ of radii 2 r and r respectively, touch each other internally at A. A chord AB…2022
• In Figure 4, two circles with centres at O and O' of radii 2 r and r respectively, touch each other internally at A. A chord AB…2022
• In Figure 1, a triangle ABC with ∠ B=90^° is shown. Taking AB as diameter, a circle has been drawn intersecting AC at point P.…2022
• Prove that a parallelogram circumscribing a circle is a rhombus.2022

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