Problem 26: Isosceles Right Triangle

Problem 26

ABC is an isosceles right triangle, where C = 90°. Points D and E are chosen on AC and BC such that CD = CE. Perpendiculars from C and D to AE meet the hypotenuse AB at F and G. Prove that:

BF = GF

Here’s a simulation that illustrates the problem.

Try dragging the A, C, and D. Are BF and GF always equal? How can we prove the same?

Solution

[coming soon]

Problem Source: CutTheKnot

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