MathDB
midpoint wanted, 2 circles realted

Source: 2013 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p11

April 27, 2021
geometrymidpointUkraine Correspondence

Problem Statement

Given a triangle ABCABC. The circle ω1\omega_1 passes through the vertex BB and touches the side ACAC at the point AA, and the circle ω2\omega_2 passes through the vertex CC and touches the side ABAB at the point AA. The circles ω1\omega_1 and ω2\omega_2 intersect a second time at the point DD. The line ADAD intersects the circumcircle of the triangle ABCABC at point EE. Prove that DD is the midpoint of AEAE..
Back to ProblemsView on AoPS