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TOT 325 1992 Spring Α J2 ADE is right iff c:b:a =3 : 4 : 5

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June 9, 2024
geometryright triangleratio

Problem Statement

Consider a right triangle ABCABC, where AA is the right angle, and AC>ABAC > AB. Points EE on ACAC and DD on BCBC are chosen so thatAB=AE=BD AB = AE = BD. Prove that the triangle ADEADE is right if and only if the ratio AB:AC:BCAB : AC : BC of sides of the triangle ABCABC is 3:4:53 : 4 : 5.
(A. Parovan)
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