1970 AHSME Problems/Problem 27

Problem

In a triangle, the area is numerically equal to the perimeter. What is the radius of the inscribed circle?

$\text{(A) } 2\quad \text{(B) } 3\quad \text{(C) } 4\quad \text{(D) } 5\quad \text{(E) } 6$

Solution

One of the most common formulas involving the inradius of a triangle is $A = rs$ , where $A$ is the area of the triangle, $r$ is the inradius, and $s$ is the semiperimeter.

The problem states that $A = p = 2s$ . This means $2s = rs$ , or $r = 2$ , which is option $\fbox{A}$ .

1970 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 26	Followed by Problem 28
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1970 AHSME Problems/Problem 27

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