MathDB

2019.1

Part of Swiss NMO - geometry

Problems(1)

fixed point, intersection of line with circle

Source: Switzerland - Swiss ΜΟ 2019 p1

7/14/2020
Let AA be a point and let k be a circle through AA. Let BB and CC be two more points on kk. Let XX be the intersection of the bisector of ∠ABC\angle ABC with kk. Let YY be the reflection of AA wrt point XX, and DD the intersection of the straight line YCYC with kk. Prove that point DD is independent of the choice of BB and CC on the circle kk.
geometryFixed pointfixedcircle