A triangle with an angle C equal to 90 degrees is inscribed in a circle, with AC = 8cm, BC = 6cm. Then the radius of the circle is?
| February 9, 2021 | education
If a right-angled triangle is inscribed in a circle, then the center of the circle is the midpoint of the hypotenuse of the triangle, then AB = D.
Using the Pythagorean theorem in a right-angled triangle ABC, we determine the length of the hypotenuse AB.
AB ^ 2 = BC ^ 2 + AC ^ 2 = 8 ^ 2 + 6 ^ 2 = 64 + 36 = 100.
AB = 10 cm.
Then R = AB / 2 = 10/2 = 5 cm.
Answer: The radius of the circle is 5 cm.
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