Question

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

Answer 1

For circle with centre as M, we have $RQ ×RP= RS^{2}$ and for circle with centre N we have $RQ\times RP= RT^{2}$.
Comparing the two, we get RS=RT

Answer 2

RS is a tangent segment and RQP is the secant ...................... (by tangent decant property )
RS² = RQ >< RP ----------- (i)
Similarly,
RT is a tangent segment and RQP is secant .
RT² = RQ >< RP ------------(II)
From (I) and (II)
RS² = RT²
RS = RT ------------------ ( taking square root )