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SAMC

Saudi Arabia geometry

Problem

Quadrilateral with perpendicular diagonals and is inscribed in a circle. Altitude in triangle intersects diagonal in . Prove that .

problem
Solution


is the orthocenter of , that is . We have ( is cyclic) and . Also, . It follows, , i.e. .

Techniques

Quadrilaterals with perpendicular diagonalsCyclic quadrilateralsTriangle centers: centroid, incenter, circumcenter, orthocenter, Euler line, nine-point circleAngle chasing