Question

Two circles touch externally at a point P. from a point T on the tangent at P, tangents TQ and TR are drawn to the circles with points of contact Q and E respectively. Prove that TQ = TR.

Answer 1

Let the circles be represented by (i) & (ii) respectively

TQ, TP are tangents to (i)

TP, TR are tangents to (ii)

We know that

The tangents drawn from external point to the circle will be equal in length.

For circle (i), TQ = TP …. (i)

For circle (ii), TP = TR …. (ii)

From (i) & (ii) TQ = TR