triangle ABC,AP perpendicular BC, BR perpendicular AC,CQ perpendicular AB

Question

prove that: Angle OPQ = angle OPR . TRY for only math genius

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Deepak Sharma · Answer

As the two right triangles ABR and APB are on the same side of AB and which is also the hypotenuse of both , the circle drawn taking AB as diameter will pass through R and P. So ABPR is a cyclic quadrilateral. Hence ∠ RPC =∠BAR Similarly ACPQ is also cyclic quadrilateral So   ∠ BPQ =∠QAC But ∠BAR =∠QAC So ∠ RPC=∠ BPQ =>90- ∠ RPC=90-∠ BPQ => ∠ OPQ =∠OPR