Question

Two circles touch each other externally at point P. Q is a point on the common tangent through P. Prove that the tangents QA and QB are equal.

Answer 1

We know tangents from external point to circle are circle,

So,

$\Rightarrow AQ=QP\left(1\right)$

$QB=QP\left(2\right)$

From $1$ and $2$

$\Rightarrow AQ=QB$

Hence, proved.