// lines connecting 2 centers, # - All-Russian MO 2001 Regional (R4) 10.2
Source:
September 26, 2024
geometryparallelparallelogram
Problem Statement
In parallelogram , point is marked on diagonal . Circle passes through point and touches lines and ( intersects the diagonal for the second time on the segment ). Circle passes through point and touches lines and ( intersects for the second time diagonal on segment ). Prove that for all positions of the point on the diagonal , the straight lines connecting the centers of circles and , will be parallel to each other.