AMC 12 Mock Exam 4 Problem 3

Problem 3 of 25

A right triangle has legs of lengths $20$ and $21$ . What is the radius of the circle inscribed in the triangle?

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Solution

The hypotenuse is $\sqrt{20^2+21^2}=\sqrt{841}=29$ . In a right triangle the tangent lengths from the right-angle vertex both equal $r$ , so $(20-r)+(21-r)=29$ , giving $r=\frac{20+21-29}{2}=\boxed{6}$ . (Check with area: $\frac12\cdot20\cdot21=210=r\cdot s=6\cdot35$ .)

Tagged: right triangle inradius

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