MathDB

9.2

Part of 2006 Sharygin Geometry Olympiad

Problems(1)

euler circles tangent to a fixed circle

Source: Sharygin 2006 finals 9.2

9/12/2019
Given a circle, point AA on it and point MM inside it. We consider the chords BCBC passing through MM. Prove that the circles passing through the midpoints of the sides of all the triangles ABCABC are tangent to a fixed circle.
Euler CircleNine Point Circlegeometryfixedcircle