Answer to Question #143564 in Geometry for J

Question #143564
. 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
1
Expert's answer
2020-11-12T19:24:59-0500

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

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

so OAP=OBP.\triangle OAP=\triangle OBP.

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

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

Q.E.D.


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