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Romania NMO 2022 Grade 9 P2

Source: Romania National Olympiad 2022

April 21, 2022
romaniageometrytrigonometry

Problem Statement

Let ABCABC be a right triangle with ∠A=90∘.\angle A=90^\circ. Let A′A' be the midpoint of BC,BC, MM be the midpoint of the height ADAD and PP be the intersection of BMBM and AA′.AA'. Prove that tan⁡∠PCB=sin⁡C⋅cos⁡C.\tan\angle PCB=\sin C\cdot\cos C.
Daniel Văcărețu
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