MathDB

2

Part of 2004 Junior Balkan MO

Problems(1)

One from Junior Balkan 2004

Source: JbMO 2004, PROBLEM 2

7/20/2004
Let ABCABC be an isosceles triangle with AC=BCAC=BC, let MM be the midpoint of its side ACAC, and let ZZ be the line through CC perpendicular to ABAB. The circle through the points BB, CC, and MM intersects the line ZZ at the points CC and QQ. Find the radius of the circumcircle of the triangle ABCABC in terms of m=CQm = CQ.
geometrycircumcirclesymmetryangle bisectorperpendicular bisectorgeometry proposed