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# right triangle

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Find the perimeter of the right triangle. The sides of the triangle are tangent to the circle.

Mar 21, 2021

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Lines that are tangent to a circle and meet at a point are congruent, as shown in the graph:

According to the Pythagorean theorem,

$$14^2+(4+x)^2=(x+10)^2\\ 196+16+8x+x^2=x^2+20x+100\\ 112=12x\\ x=\frac{112}{12}=\boxed{\frac{28}{3}}$$

Mar 21, 2021