A triangle is inscribed in a circle so that its center lies on one of the sides of the triangle.

| January 18, 2021 | education

A triangle is inscribed in a circle so that its center lies on one of the sides of the triangle. Find the radius of the circle if the other two sides are 6 and 8 cm.

According to the condition, one of the sides of the triangle passes through the center of the circle, therefore, this side is the diameter of the circle and the hypotenuse of the right triangle, since if one of the sides of the triangle is the diameter of the circle, then the inscribed triangle is right-angled.

Let ABC be an inscribed triangle with a straight angle C, leg AC = 6 cm, CB = 8 cm, according to the condition.

By the Pythagorean theorem, the hypotenuse AB will be equal to.

AB ^ 2 = AC ^ 2 + BC ^ 2 = 6 ^ 2 + 8 ^ 2 = 36 * 64 = 100. AB = 10 cm.

Then the radius of the circle will be equal to: OA = AB / 2 = 10/2 = 5 cm.

Answer: The radius of the circle is 5 cm.



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