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Difference between revisions of "2023 SSMO Team Round Problems/Problem 3"

(Created page with "==Problem== Let <math>ABC</math> be a triangle such that <math>AB=4\sqrt{2}, BC=5\sqrt{2},</math> and <math>AC=\sqrt{82}.</math> Let <math>\omega</math> be the circumcircle of...")
(No difference)

Revision as of 22:25, 15 December 2023

Problem

Let $ABC$ be a triangle such that $AB=4\sqrt{2}, BC=5\sqrt{2},$ and $AC=\sqrt{82}.$ Let $\omega$ be the circumcircle of $\triangle ABC$. Let $D$ be on the circle such that $\overline{BD} \perp \overline{AC}.$ Let $E$ be the point diametrically opposite of $B$. Let $F$ be the point diametrically opposite $D$. Find the area of the quadrilateral $ADEF$ in terms of a mixed number $a\frac{b}{c}$. Find $a+b+c$.

Solution

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