Question

11. Two circles intersect each other in
points A and B. Seg AB is the
chord of both the circles. Point C
is in the exterior point of both the
circles on the line AB. From the
point C tangents are drawn to the
circles touching at M and N as
shown. Complete the following to
prove CM = CN.​

Answer 1

Line CBA is a secant intersecting the circle at point B and A and line CM is a tangent at point M.

∴ CM² = CB×CA .....(i)

Line CBA is a secant intersecting the circle at point B & A and line CN is a tangent at point N.

∴ CN² = CB×CA ......(ii)

From equations (i) and (ii), we have

CM²=CN²

Taking square roots on both sides

∴CM=CN

Hence, proved