EXERCISE 10.2 — NCERT Solutions for Class 10 Mathematics Chapter 10

EXERCISE 10.2 1–13 (part 2 of 2)

In Q. $\displaystyle 1$ to $\displaystyle 3$, choose the correct option and give justification.
Exercise 1
From a point Q , the length of the tangent to a circle is $\displaystyle 24$ cm and the distance of Q from the centre is $\displaystyle 25$ cm. The radius of the circle is (A) $\displaystyle 7$ cm (B) $\displaystyle 12$ cm (C) $\displaystyle 15$ cm (D) $\displaystyle 24.5$ cm
NCERT’s answer
A
Working being prepared
Exercise 2
In Fig. $\displaystyle 10.11$ , if TP and TQ are the two tangents to a circle with centre O so that $\displaystyle \angle \mathrm{POQ}=110^{\circ}$ , then $\displaystyle \angle \mathrm{PTQ}$ is equal to (A) $\displaystyle 60$ ° (B) $\displaystyle 70$ ° (C) $\displaystyle 80$ ° (D) $\displaystyle 90$ °
NCERT’s answer
B
Working being prepared
Exercise 3
If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of $\displaystyle 80$ °, then $\displaystyle \angle \mathrm{POA}$ is equal to (A) $\displaystyle 50$ ° (B) $\displaystyle 60$ ° (C) $\displaystyle 70$ ° (D) $\displaystyle 80$ °
NCERT’s answer
A
Working being prepared
Exercise 4
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Solution being prepared
Exercise 5
Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
Solution being prepared
Exercise 6
The length of a tangent from a point A at distance $\displaystyle 5$ cm from the centre of the circle is $\displaystyle 4$ cm. Find the radius of the circle.
NCERT’s answer
$\displaystyle 3$ cm
Working being prepared
Exercise 7
Two concentric circles are of radii $\displaystyle 5$ cm and $\displaystyle 3$ cm . Find the length of the chord of the larger circle which touches the smaller circle.
NCERT’s answer
$\displaystyle 8$ cm
Working being prepared
Exercise 8
A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. $\displaystyle 10.12$ ). Prove that $A B+C D=A D+B C$
Solution being prepared
Exercise 9
In Fig. $\displaystyle 10.13$ , XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and $\displaystyle \mathrm{X}^{\prime} \mathrm{Y}^{\prime}$ at B . Prove that $\displaystyle \angle \mathrm{AOB}=90^{\circ}$ .
Solution being prepared
Exercise 10
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
Solution being prepared
Exercise 11
Prove that the parallelogram circumscribing a circle is a rhombus.
Solution being prepared
Exercise 12
A triangle ABC is drawn to circumscribe a circle of radius $\displaystyle 4$ cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths $\displaystyle 8$ cm and $\displaystyle 6$ cm respectively (see Fig. $\displaystyle 10.14$ ). Find the sides AB and AC.
NCERT’s answer
$\displaystyle \mathrm{AB}=15 \mathrm{~cm}, \mathrm{AC}=13 \mathrm{~cm}$
Working being prepared
Exercise 13
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
Solution being prepared