MathDB

6

Part of 2019 Costa Rica - Final Round

Problems(1)

collinear wanted, starting with right isosceles triangle

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2019 3.6

9/21/2021
Consider the right isosceles △ABC\vartriangle ABC at A A. Let LL be the intersection of the bisector of ∠ACB\angle ACB with ABAB and KK the intersection point of CLCL with the bisector of BCBC. Let XX be the point on line AKAK such that ∠KCX=90o\angle KCX = 90^o and let YY be the point of intersection of CXCX with the circumcircle of △ABC\vartriangle ABC. Let Y′Y' the reflection of point YY wrt BCBC. Prove that B−K−Y′B - K -Y'.
Notation: A−B−CA-B-C means than points A,B,CA,B,C are collinear in that order i.e. B B lies between A A and CC.
geometryisoscelesright trianglecollinear