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

Answer:

Step-by-step explanation:

Hi,

Given circles with centers a M and N.

Given points of intersection of two circles are at P and Q,

Let us chose a point R on the line joining P and Q as shown

Let us draw tangents from R to both the circles touching at M

and N respectively,

Consider circle with center M, we can observe that RPQ is the

secant of the circle and RS is the tangent to the circle,

So from secant tangent property,

RS² = RP * RQ    -----(1)

Consider circle with center N, we can observe that RPQ is the

secant of the circle and RT is the tangent to the circle,

So from secant tangent property,

RT² = RP * RQ    -----(2),

From (1) and (2),

RS² = RP * RQ = RT²

Hence, RS = RT.

Hope, it helps !