MathDB

31

Part of 2013 Harvard-MIT Mathematics Tournament

Problems(1)

2013 HMMT Guts #31: Quadrilateral in Unit Circle

Source:

3/26/2013
Let ABCDABCD be a quadrilateral inscribed in a unit circle with center OO. Suppose that ∠AOB=∠COD=135∘\angle AOB = \angle COD = 135^\circ, BC=1BC=1. Let B′B^\prime and C′C^\prime be the reflections of AA across BOBO and COCO respectively. Let H1H_1 and H2H_2 be the orthocenters of AB′C′AB^\prime C^\prime and BCDBCD, respectively. If MM is the midpoint of OH1OH_1, and O′O^\prime is the reflection of OO about the midpoint of MH2MH_2, compute OO′OO^\prime.
HMMTgeometrygeometric transformationreflection