Question
Mon February 13, 2012 By: Ajinkya Pande

In triangleABC A is an obtuse angle.P is circumcircle of triangleABC prove that anglePBC=angleA-90degrees

Expert Reply
Mon February 13, 2012
We can see in the figure that angleBPC = 2angleA , as angle subtended by any arc at the center is twice the angle it subtends on any point at the circumference of the circle .
Also In triangle BPC , angle PBC = angle PCB
Also
anglePBC + anglePCB + angle BPC = 180
2anglePBC + 2angleA = 180
So
anglePBC = 90 - angleA
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