Question

Two concentric circles have radii 5cm and 3cm.Find the length of the chord of the larger circle which touches the smaller circle.
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

Given:


OA= 3 cm (radius of smaller circle)

OP= 5 cm (radius of bigger circle)


Let O be the center of  two concentric circles.


let PQ be the chord of the larger circle which touches the smaller circle at point A. Here, PQ is tangent to the smaller circle.

OA ⊥ PQ  (OA is the radius of the circle)

In Δ OAP,

OA²+ AP² = OP²

[ By Pythagoras theorem]

3² + AP² = 5²

9 + AP² = 25

AP² = 25-9= 16


AP²= 16

AP =√16


AP= 4 cm

In ΔOPQ,

Since OA ⊥ PQ,

AP = AQ    (Perpendicular from the center of the circle bisects the chord)

PQ = 2AP = 2 × 4 = 8

Hence, the length of the chord of the larger circle is 8 cm.


[FIGURE IS IN THE ATTACHMENT]