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Triangle xy Area

A circle is drawn that is tangent to the three sides of the triangle. The two constituent lengths of the hypotenuse are given and the challenge is to calculate the area of the triangle. When working on the numerical examples it becomes apparent that the area of the triangle is given by multiplying the lengths.

The proof of the result involves the use of Pythagoras’ theorem, areas of kites, and algebraic manipulation. A supplementary question asks ‘what is the radius of the circle touching the three sides of the triangle?’

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