Question

Find the radius of a circle inscribed in a 5-12-13 triangle.

Answer 1

Find the radius of a circle inscribed in a 5-12-13 triangle.

Solution:

Use the Pythagorean theorem to see whether this triangle is right:

$$a^{2} + b^{2} = c^{2}$$ $$5^{2} + 12^{2} = 13^{2} \Rightarrow 169 = 169$$

Let $r$ be radius, $S$ – area of the triangle, $p$ – half of perimeter

$$r = \frac{S}{p}$$ $$S = \frac{1}{2}ab = \frac{1}{2} \cdot 5 \cdot 12 = 30$$ $$p = \frac{5 + 12 + 13}{2} = 15$$ $$r = \frac{30}{15} = 2$$

Answer: radius of an inscribed circle equals 2.