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An American Mathematics Monthly Problem

Given triangle ABC, squares are constructed on each side, and parallelograms connected to the squares as shown below.

The problem is to show that the resulting triangle AKJ is an isosceles right triangle for any original triangle. A,B,C may be dragged in the drawing for numerical validation of the assertion.

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AJ
angle JAK
AK

The problem can be found in American Mathematical Monthly,
Vol 75 p 899 problem E2124.

App generated by Geometry Expressions