MathDB

2

Part of 1984 Balkan MO

Problems(1)

congruent quadrilaterals

Source: bmo 1984

4/23/2007
Let ABCDABCD be a cyclic quadrilateral and let HA,HB,HC,HDH_{A}, H_{B}, H_{C}, H_{D} be the orthocenters of the triangles BCDBCD, CDACDA, DABDAB and ABCABC respectively. Show that the quadrilaterals ABCDABCD and HAHBHCHDH_{A}H_{B}H_{C}H_{D} are congruent.
geometryparallelogramcircumcircleratiogeometric transformationhomothetyreflection