Geometry problem (nine-point circle?)

stephanson12

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Dec 16, 2023
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Let △ABC be a triangle with a circumscribed circle Γ with center O and orthocenter H. Take that AB ̸= AC and ∠A ̸= π/2. Let M and N be the centers of [AB] and [AC] respectively, and let E and F be the feet of the altitudes from B and C in △ABC, respectively. Let P be the intersection of MN and the tangent to Γ in A. Let Q be the intersection (different from A) of Γ with the circumscribed circle of △AEF. Finally, let R be the intersection of AQ and EF. Prove that PR ⊥ OH.

Hello, can someone please help me with this exercise? You should not solve it, but just give a hint. I just don't know how to start because a lot of information has been given. Sorry for my bad english
 
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