# The tangents to a circle are equal in length

Submitted by Isoscel on Sat, 09/01/2007 - 16:14.

If P is a point in the exterior of the circle C, then if M and N are on C so that PM and PN are tangent with C we have:

Indeed,

as both are right triangles,OP is common and OM=ON=radius

Then all others correspondent elements are congruent.PM=PN

Also we have PO is the bisector of angle MPN