Question

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

Answer 1

From Q, QA and QP are two tangents to the circle with centre O

Therefore, QA = QP  ...(i)

Similarly, from Q, QB and QP are two tangents to the circle with centre O'

Therefore, QB = QP ...(ii)

From (i) and (ii)

QA = QB

Therefore, tangents QA and QB are equal.