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obtuse wanted, if < BAC >=60^o

Source: VI Soros Olympiad 1990-00 R3 10.2 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 28, 2024
anglesgeometry

Problem Statement

In the triangle ABCABC, the point XX is the projection of the touchpoint of the inscribed circle to the side BCBC on the middle line parallel to BCBC. It is known that ∠BAC≥60o\angle BAC \ge 60^o. Prove that the angle BXCBXC is obtuse.
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