MathDB

3

Part of 2019 Pan-African

Problems(1)

PAMO Problem 3: Circumcentres coincide implies equilateral

Source: 2019 Pan-African Mathematics Olympiad, Problem 3

4/9/2019
Let ABCABC be a triangle, and DD, EE, FF points on the segments BCBC, CACA, and ABAB respectively such that BDDC=CEEA=AFFB. \frac{BD}{DC} = \frac{CE}{EA} = \frac{AF}{FB}. Show that if the centres of the circumscribed circles of the triangles DEFDEF and ABCABC coincide, then ABCABC is an equilateral triangle.
geometryCircumcenterPAMOEquilateral Trianglecircumcircle