Given a right-angled triangle ABC side AC = 8, BC = 6 find R and r.
| May 7, 2021 | education
Let ABC be a given triangle (∠C = 90 °).
By the Pythagorean theorem AB ^ 2 = AC ^ 2 + CB ^ 2.
AB ^ 2 = 8 ^ 2 + 6 ^ 2 = 64 + 36 = 100.
AB = 10.
Because the angle based on the diameter is a straight line, then the hypotenuse of the triangle ABC is the diameter of the circle described around this triangle.
AB = 2R,
R = ½ AB = ½ * 10 = 5.
To find the radius r of a circle inscribed in a triangle, use the formula S = 1/2 (AB + BC + AC) * r.
½ (AB + BC + AC) = ½ (10 + 6 + 8) = ½ * 24 = 12.
S = 12r.
Knowing the area of the triangle, one can find r /
S = ½ CB * AC = ½ * 6 * 8 = 24.
24 = 12r;
r = 24: 12 = 2.
Answer: R = 5, r = 2.
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