A right-angled triangle is inscribed in a circle with a radius of 13 cm. Calculate the larger leg if the smaller one is 10 cm.
| April 5, 2021 | education
Since a right-angled triangle is inscribed in a circle, its hypotenuse coincides with the diameter of the circle.
By condition, OA = R = 13 cm, then AB = 2 * OA = 2 * 13 = 26 cm.
Their right-angled triangle ABC, according to the Pythagorean theorem, determine the length of the leg AC.
AC ^ 2 = AB ^ 2 – BC ^ 2 = 26 ^ 2 – 10 ^ 2 = 676 – 100 = 576.
AC = 24 cm.
Answer: The length of the larger leg is 24 cm.
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