CN-TST 2014 Problem 10

Given circle $O$ with radius $R$ , the inscribed triangle $ABC$ is an acute scalene triangle, where $AB$ is the largest side. $AH_A, BH_B,CH_C$ are heights on $BC,CA,AB$ . Let $D$ be the symmetric point of $H_A$ with respect to $H_BH_C$ , $E$ be the symmetric point of $H_B$ with respect to $H_AH_C$ . $P$ is the intersection of $AD,BE$ , $H$ is the orthocentre of $\triangle ABC$ . Prove: $OP\cdot OH$ is fixed, and find this value in terms of $R$ .

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