MathDB

2013.11

Part of Ukraine Correspondence MO - geometry

Problems(1)

midpoint wanted, 2 circles realted

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

4/27/2021
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..
geometrymidpointUkraine Correspondence