two circles touch each other externally. prove that the lengths of the tangents drawn to the circle from any point on the common tangent are equal.

please help it is a bit urgent!

Given   Two circles with centre O and O' touch each other externally and let the point where they touch each other be M.
PM is the common tangent.Let a point P on the common tangent from where tangents PA and PB are drawn to the circles having centres O and O' respectively.
To prove  PA = PB

$$\begin{gathered} Now as we know that \tan gents drawn from an external point to a circle are equal in length \\ Hence consider the circle having centre O \\ P is an external point and let \tan gents drawn from the point P are PA and PM \\ \therefore PA = PM ..........\left(1\right) \\ Now consider the circle having centre O\text{'} \\ P is an external point and let \tan gents drawn from the point P are PB and PM \\ \therefore PB=PM........\left(2\right) \\ Hence from \left(1\right) and \left(2\right) we can say that \\ PA=PB \\ \therefore Lengths of the tangents drawn to the circle from any point on the common \tan gent are equal \end{gathered}$$