Question

Two circle touch each other internally. Show that the tangents drawn to the two circles from any point on the common tangent are equal in length.

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.