Answer to Question #143564 in Geometry for J

Question

. Prove the corollary of the tangent theorem: If A and B are points on
circle O and line segments PA and PB are tangent to the circle, show that line segment PA is congruent to line segment PB
and line segment PO bisects angle APB

Answer 1

$\angle OAP=\angle OBP=90\degree,$

$OA=OB$ like radiuses, OP is common side,

so $\triangle OAP=\triangle OBP.$

So $AP=BP$ and $\angle APO=\angle BPO.$

Line segment PA is congruent to line segment PB and line segment PO bisects angle APB.

Q.E.D.