similar triangles

The following geometry problem is simple to state but challenging to solve!

Elegant proofs of mathematical statements present the beauty of mathematics and enhance our learning pleasure. This is particularly so for ‘proofs without words’ which significantly improve the visual proof capability. In this article, we present three largely visual proofs which carry a great deal of elegance. In a strict sense they are not pure proofs without words because of the mathematical expressions and formulas that appear in them. Nevertheless, they carry a lot of appeal.

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