We say that a triangle ABC is great if the following holds: for any point D on the side BC, if P and Q are the feet of the perpendiculars from D to the lines AB and AC, respectively, then the reflection of D in the line PQ lies on the circumcircle of the triangle ABC. Prove that triangle ABC is great if and only if ∠A=90∘ and AB=AC.Senior Problems Committee of the Australian Mathematical Olympiad Committee geometrycircumcircleAPMOgeometry solvedfunctional equationright trianglereflection