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computational geo, right triangle, another right angle

Source: 2021 Dürer Math Competition Finals Day2 E+1 https://artofproblemsolving.com/community/c2749870_

January 9, 2022
geometryright triangle

Problem Statement

Given a right angled triangle ABCABC in which ∠ACB=90o\angle ACB = 90^o. Let DD be an inner point of ABAB, and let EE be an inner point of ACAC. It is known that ∠ADE=90o\angle ADE = 90^o, and that the length of the segment ADAD is 88, the length of the segment DEDE is 1515, and the length of segment CECE is 33. What is the area of triangle ABCABC?
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