Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 5.5 AIME, harder Prove it

The vertices $X, Y, Z$ of an equilateral triangle $X Y Z$ lie respectively on the sides $B C$ , $C A, A B$ of an acute-angled triangle $A B C$ . Prove that the incenter of triangle $A B C$ lies inside triangle $X Y Z$ .

Solution

None

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None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.