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O is the orthocentre of △ABC if and only if AP⊥BC, BR⊥AC and CQ⊥AB. Prove that angle OPQ= angle OPR

bhuwan budhathoki
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  • What are $P$, $Q$, and $R$? How are they related to $O$? – Batominovski Sep 09 '18 at 02:39
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This is only angle chasing, $\angle OPC=90^{\circ}$. Also, $\angle RPC =BAC$ because $ARPB$ is a cyclic quadrilateral. In the same way $\angle QPB = \angle BAC$. From this point, the conclusion follows.enter image description here

Ricardo Largaespada
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