MathDB
triangle, interior angle bisector, circumcenter, incenter

Source:

March 5, 2005
geometrycircumcircleincenterratioquadraticsangle bisectorperpendicular bisector

Problem Statement

In the triangle ABCABC let ADAD be the interior angle bisector of ∠ACB\angle ACB, where D∈ABD\in AB. The circumcenter of the triangle ABCABC coincides with the incenter of the triangle BCDBCD. Prove that AC2=AD⋅ABAC^2 = AD\cdot AB.
Back to ProblemsView on AoPS