167. Inscribed Circles. Which of the two triangles has a larger inscribed circle: the triangle with sides 17, 25, and 26, or the triangle with sides 17, 25, and 28?
167. Answer: none. The radius of the inscribed circle of a triangle with sides $a, b, c$ is calculated by the formula

$$
r=\frac{S}{p}=\left[\frac{(p-a)(p-b)(p-c)}{p}\right]^{\frac{1}{2}}, \quad \text { where } \quad 2 p=a+b+c
$$

From this, for each of our triangles, the radius value will be 6.

A rare example of "obtuse twins" are triangles with sides equal to $97,169,122$ and 97,169, 228. Each of them has an inscribed circle radius of 30.

[B. H. Brown, M. M., 29, 275-276 (May 1956).]

![](https://cdn.mathpix.com/cropped/2024_05_21_2b40d984baf9da275c68g-130.jpg?height=556&width=537&top_left_y=316&top_left_x=765)