Two circle touch each externally at point P. Q is a point on the common tangent through P. Then, the tangents QA and QB are equal.

True

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False

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Solution

The correct option is A
True

Given - Two circle with centre O and O' touches at P externally. Q is a point on the common tnagent through P. QA and QB are tangents from Q to the circle respectively.

To Prove - QA = QB.

Proof - From Q, QA and QP are the tangents to the circle with centre O.

$∴$ QA = QP .....(i)

Similarly, QP and QB are the tangens to the circle with centre O'

$∴$ QP = QB .....(ii)

From (i) and (ii)

QA = QB Q.E.D

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