MathDB
fixed point for circumcircle, equal angles (2020 Kyiv City MO 9.4)

Source:

September 20, 2020
geometrycircumcirclefixedFixed pointequal angles

Problem Statement

Let the point DD lie on the arc ACAC of the circumcircle of the triangle ABCABC (AB<BCAB < BC), which does not contain the point BB. On the side ACAC are selected an arbitrary point XX and a point X′X' for which ∠ABX=∠CBX′\angle ABX= \angle CBX'. Prove that regardless of the choice of the point XX, the circle circumscribed around △DXX′\vartriangle DXX', passes through a fixed point, which is different from point DD.
(Nikolaev Arseniy)
Back to ProblemsView on AoPS