Problem for April 12th from the 2026 AMS Daily Epsilon of Math Calendar

@DailyEpsilon

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@PercyButtons3 @DailyEpsilon

One could certainly use Heron for this, after solving for the lengths of the sides, but a sharp eye should be able to recognize a very famous triangle hidden in the given isosceles triangle.

@tpfto @PercyButtons3 @DailyEpsilon What's this Heron you're referring to?
Heron's formula - Wikipedia