In Figure, `X Pa n dX Q` are tangents from `X` to the circle with centre `OdotR` is a point on the circle. Prove that, `X A+A R=X B+B R`

Explanation

We know that the lengths of tangents drawn from a exterior point to a circle are equal.
`:.XP=XQ`, ………`(i)`[tangents from `X`]
`AP=AR`, ………`(ii)` [tangents from `A`]
`BR=BQ`. ………..`(iii)` [tangents from `B`]
Now, `XP=XQimpliesXA+AP=XB+BQ`
`impliesXA+AR=XB+BR` [using `(ii)` and `(iii)`].