The triangle is inscribed in a circle with a radius of 4 cm. Find the largest side of the triangle if the center of the circumscribed circle lies on the side of the triangle.
Since the center of the circle, point O, lies on one of the sides of the inscribed triangle, the opposite angle of this triangle rests on the diameter of the circle, and therefore is equal to half the degree measure of the arc on which it rests. Angle BAC = 180/2 = 90.
Then the triangle ABC, inscribed in a circle, is rectangular, and its hypotenuse is equal to the diameter of the circle.
Since the hypotenuse of a right-angled triangle is larger than its legs, the largest side of the BC = 2 * R = 2 * 4 = 8 cm.
Answer: The longest side of the triangle is 8 cm.
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