MathDB
France TST 2007

Source: ISL 2006, G4, France TST 2007/6 1st Brazilian TST 2007, AIMO 2007, TST 4, P1

May 16, 2007
geometryincenterTriangleIMO Shortlistgeometry solvedmidpointcongruent triangles

Problem Statement

A point DD is chosen on the side ACAC of a triangle ABCABC with ∠C<∠A<90∘\angle C < \angle A < 90^\circ in such a way that BD=BABD=BA. The incircle of ABCABC is tangent to ABAB and ACAC at points KK and LL, respectively. Let JJ be the incenter of triangle BCDBCD. Prove that the line KLKL intersects the line segment AJAJ at its midpoint.
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