MathDB

3#

Part of 2020 Middle European Mathematical Olympiad

Problems(1)

exists a circle tangent to three others

Source: 2020 MEMO I-3

8/30/2020
Let ABCABC be an acute scalene triangle with circumcircle ω\omega and incenter II. Suppose the orthocenter HH of BICBIC lies inside ω\omega. Let MM be the midpoint of the longer arc BCBC of ω\omega. Let NN be the midpoint of the shorter arc AMAM of ω\omega. Prove that there exists a circle tangent to ω\omega at NN and tangent to the circumcircles of BHIBHI and CHICHI.
geometrycircumcircleincentermemoMEMO 2020