right angle triangle with circumcircle, Toricelli point lies on circumcircle
Source: Bulgaria 1967 P3
June 23, 2021
geometrycircumcircle
Problem Statement
It is given a right-angled triangle and its circumcircle .
(a) prove that the radii of the circle tangent to the cathets of the triangle and to the circle is equal to the diameter of the incircle of the triangle ABC.
(b) on the circle there may be found a point for which the sum is as large as possible.