Two circles touch externally at a point P. From a point T on the tangent at P, tangents TQ and T on the tangent at P

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 R respectively. Prove that TQ = TR

Answer 1

Let us label two circles as 'a' and 'b

As TQ and TP are tangents to circle a,And TP and TR are tangents to circle b.

By theorem which states that the lengths of the two tangents drawn from external point to a circle are equal.

TQ=TP ...(1)

TP=TR ...(2)

From 1 and 2,

TQ=TR

Hence proved