Circles

CBSE Class 10 Mathematics · every board question from this chapter, 2025–2025 · 23 of them repeated across years

• 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:2025asked 2×
• 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:2025asked 3×
• 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…2025asked 3×
• 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…2025asked 3×
• Which of the following statements is false?2025asked 3×
• For a circle with centre O and radius 5 cm, which of the following statements is true? P: Distance between every pair of parallel…2025asked 3×
• In the adjoining figure, PA and PB are tangents to a circle with centre O. The measure of angle APB is2025asked 3×
• In the adjoining figure, TS is a tangent to a circle with centre O. The value of 2 x^° is2025asked 2×
• 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…2025asked 3×
• A parallelogram having one of its sides 5 cm circumscribes a circle. The perimeter of parallelogram is:2025asked 3×
• 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:2025asked 3×
• Assertion: A line drawn perpendicular to the tangent at point of contact passes through the centre of the circle. Reason (R):…2025
• Assertion: If two tangents are drawn to a circle from an external point, then they subtend equal angles at the centre of the…2025asked 3×
• 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,…2025asked 2×
• 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…2025asked 3×
• 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…2025asked 3×
• Prove that the tangents drawn at the ends of a diameter of a circle are parallel.2025asked 3×
• 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…2025asked 3×
• Prove that the parallelogram circumscribing a circle is a rhombus. OR Prove that the angle between the two tangents drawn from an…2025asked 3×
• 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…2025asked 3×
• 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 ∠…2025asked 2×
• Rectangle ABCD circumscribes the circle of radius 10 cm. Prove that ABCD is a square. Hence, find the perimeter of ABCD.2025asked 3×
• 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…2025asked 3×
• 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…2025asked 3×

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