Sharygin Olympiads, the best
Igor Fedorovich Sharygin (13/02/1937 - 12/03/2004, Moscow) - Soviet and Russian mathematician and teacher, specialist in elementary geometry, popularizer of science. He wrote many textbooks on geometry and created a number of beautiful problems. He headed the mathematics section of the Russian Soros Olympiads. After his death, Russia annually hosts the Geometry Olympiad for high school students. It consists of two rounds – correspondence and final. The correspondence round lasts 3 months.
The best problems of these Olympiads will be published. The numbering contains the year of the Olympiad and the serial number of the problem. Solutions are often different from the original ones.
2024, Problem 23
A point moves along a circle
Let
and
be fixed points of
and
be an arbitrary point inside
The common external tangents to the circumcircles of triangles
and
meet at point
Prove that all points
lie on two fixed lines.
Solution