MathDB
2018 PUMaC Live Round 8.2

Source:

January 13, 2019
PuMACLive Roundgeometrycircumcircle

Problem Statement

The triangle ABCABC satisfies AB=10AB=10 and has angles ∠A=75∘\angle{A}=75^{\circ}, ∠B=60∘\angle{B}=60^{\circ}, and ∠C=45∘\angle C = 45^{\circ}. Let IAI_A be the center of the excircle opposite AA, and let DD, EE be the circumcenters of triangle BCIABCI_A and ACIAACI_A respectively. If OO is the circumcenter of triangle ABCABC, then the area of triangle EODEOD can be written as abc\tfrac{a\sqrt{b}}{c} for square-free bb and coprime a,ca,c. Find the value of a+b+ca+b+c.
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