Question

In the given figure, there are two circles with the centres O and O' touching each other internally at P. Tangents TQ and TP are drawn to the larger circle and tangents TP and TR are drawn to the smaller circle . Find TQ : TR

• A. 8 : 7
• B. 7 : 8
• C. 5 : 4
• D. 1 : 1

Answer 1

The correct option is D

1 : 1

As the lengths of tangents drawn from an external point to a circle are equal,

For the circle with center O, TQ = TP ….(i)

For the circle with center $O^{{}^{\prime }}$, TR = TP ….(ii)

Dividing equation (i) by (ii), we get,

TQ : TR = 1 : 1