MathDB
2019 Fall Team #4

Source:

April 17, 2022
geometry

Problem Statement

Let △ABC\vartriangle ABC be a triangle such that the area[ABC]=10 [ABC] = 10 and tan⁡(∠ABC)=5\tan (\angle ABC) = 5. If the smallest possible value of (AC‾)2(\overline{AC})^2 can be expressed as −a+bc-a + b\sqrt{c} for positive integers a,b,ca, b, c, what is a+b+ca + b + c?
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