Question

two circles with centres M and N intersect each other at P and Q. The tangents drawn from point R on the line PQ touch the circles at S and T. Prove that, RS=RT

Answer 1

in circle m
tangent rs =rq (as they orginate from same point ----1

in circle n
rq=rt----2
from 1 and 2 rs =rt

Answer 2

Answer:

The proof is explained below.

Step-by-step explanation:

Given two circles with centres M and N intersect each other at P and Q. The tangents drawn from point R on the line PQ touch the circles at S and T. we have to prove that RS=RT

By tangent secant theorem which states that when a tangent and a secant construct from one single external point to a circle then square of length of tangent must be equal to the product of lengths of whole secant segment and the exterior portion of secant segment.

RQP is a secant to a circle intersecting it at Q and P and RS is a tangent then $RS^2=RQ\times RP$

Similarly, RQP is a secant to a circle intersecting it at Q and P and RT is a tangent then $RT^2=RQ\times RP$

Hence, from above two we get $RS^2=RQ^2$

⇒ RS=RT