MathDB
Geometrical Geometry Problem

Source: KMO 2021 P6

November 13, 2021
geometrycircumcircletangent

Problem Statement

Let ABCABC be an obtuse triangle with ∠A>∠B>∠C\angle A > \angle B > \angle C, and let MM be a midpoint of the side BCBC. Let DD be a point on the arc ABAB of the circumcircle of triangle ABCABC not containing CC. Suppose that the circle tangent to BDBD at DD and passing through AA meets the circumcircle of triangle ABMABM again at EE and BD‾=BE‾\overline{BD}=\overline{BE}. ω\omega, the circumcircle of triangle ADEADE, meets EMEM again at FF.
Prove that lines BDBD and AEAE meet on the line tangent to ω\omega at FF.
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