Two circles touches internally at a point P and from a point T ,the common tangent at P , tangent segments TQ and TR are drawn to the two circle Prove that TQ=TR

Question should be:

Two circles touches externally at a point P and from a point T, the common tangent at P, tangent segments TQ and TR are drawn to the two circle Prove that TQ=TR.

 

Proof:-

Let the circles be C₁ and C₂

C₁ and C₂ touch each other externally at P

From T, tangents are drawn

Tangent TQ on C₁ and tangent TR on C₂, common tangent is TP

Since, the tangents drawn from an external point are equal, we have

TP =TQ and TP = TR

Therefore, TQ = TR.