MathDB

4

Part of 2017 Cono Sur Olympiad

Problems(1)

Circumcenter midpoint of segment

Source: Cono Sur Olympiad 2017, problem 4

8/21/2017
Let ABCABC an acute triangle with circumcenter OO. Points XX and YY are chosen such that:
[*]∠XAB=∠YCB=90∘\angle XAB = \angle YCB = 90^\circ[/*] [*]∠ABC=∠BXA=∠BYC\angle ABC = \angle BXA = \angle BYC[/*] [*]XX and CC are in different half-planes with respect to ABAB[/*] [*]YY and AA are in different half-planes with respect to BCBC[/*]
Prove that OO is the midpoint of XYXY.
geometrycono surcircumcircle