The legs of a right-angled triangle are 15 cm and 20 cm. Find the radius of its inscribed circle.
| September 10, 2021 | education
1. A, B, C – the vertices of the triangle. ∠С = 90 °. leg BC = 15 cm. leg AC = 20 cm.
2. We calculate the length of the side AB, which is a hypotenuse in a given right-angled triangle:
AB = √BC² + AC² (by the Pythagorean theorem).
AB = √BC² + AC² = √15² + 20² = √225 + 400 = 25 cm.
3. Calculate the radius (r) of a circle inscribed in a triangle by the formula:
r = (BC + AC – AB) / 2 = (15 + 20 – 25) / 2 = 10/2 = 5 cm.
Answer: the radius of a circle inscribed in a right-angled triangle ABC is 5 cm.
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