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.

8 : 7

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7 : 8

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5 : 4

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1 : 1

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Solution

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 $O^{^{'}}$ , TR = TP ….(ii)

Divide eq (i) by (ii),

$\frac{T Q}{T R} = \frac{T P}{T P}$

$∴ T Q : T R = 1 : 1$

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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

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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.

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′, TR = TP ….(ii) Divide eq (i) by (ii), TQTR=TPTP ∴TQ:TR=1:1