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2024 SSMO Relay Round 1 Problems/Problem 1

Revision as of 16:01, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>AD</math> be an altitude of triangle <math>ABC</math> and let <math>DE</math> be an altitude of triangle <math>ACD.</math> If <math>AB=29,CE=9,</math> a...")
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Problem

Let $AD$ be an altitude of triangle $ABC$ and let $DE$ be an altitude of triangle $ACD.$ If $AB=29,CE=9,$ and $DE=12,$ what is the area of triangle $ABC?$

[asy] size(200); pair A,B,C,D,EE; A = (0,20); B = (-21,0); C = (15,0); D = (0,0); EE = 0.36*A+0.64*C; draw(A--B--C--cycle); draw(A--D--EE); dot("\(A\)", A, N); dot("\(B\)", B, W); dot("\(C\)", C, E); dot("\(D\)", D, S); dot("\(E\)", EE, dir(EE)); [/asy]

Solution

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