MathDB
iff condition on AI+CD=AC where AD is the angle bisector

Source: Polish Second Round 2001

March 6, 2012
geometryincentercircumcircleperpendicular bisectorgeometry proposed

Problem Statement

In a triangle ABCABC, II is the incentre and DD the intersection point of AIAI and BCBC. Show that AI+CD=ACAI+CD=AC if and only if ∠B=60∘+13∠C\angle B=60^{\circ}+\frac{_1}{^3}\angle C.
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