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. Completely the following to prove CM= CN.
Proof `:`
`CM^(2) = CA xx square ` ....( `square `) ....(1)
`CN^(2) = square xx CB ` ...(Tangent secant segment property ) ....(2)
`:.` From (1) and (2),
`CM^(2) = square `
`:. CM = CN `

Answer

`CM^(2) = CA xx CB` …(1)
….(Tangent secant segment property)
`CN^(2) = CA xx CB` ….(2)
from (1) and (2).
`CM^(2) = CN^(2)`
`:. CM = CN`.