Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 4.5 AIME Find the answer

4. Given an acute triangle $\triangle A B C$ , and $A C<A B<B C$ . If a point $M$ on the plane of $\triangle A B C$ makes $\triangle A B M$ and $\triangle B C M$ both isosceles triangles, we call point $M$ a “regular point”. How many regular points are there?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

$\frac{4}{14}$

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