MathDB

P14

Part of 2017 Sharygin Geometry Olympiad

Problems(1)

Three circles

Source: Sharygin Geometry Olympiad Correspondence Round 2017 P-14 (Grade-9-11)

5/1/2017
Let points BB and CC lie on the circle with diameter ADAD and center OO on the same side of ADAD. The circumcircles of triangles ABOABO and CDOCDO meet BCBC at points FF and EE respectively. Prove that R2=AF.DER^2 = AF.DE, where RR is the radius of the given circle. Proposed by N.Moskvitin
geometry