In triangle ABC, angle C is 90g, AC =, BC = 4. Find the radius of the circumscribed circle of this triangle.

univerkov | July 5, 2021 | education

Since a right-angled triangle is inscribed in a circle, its hypotenuse coincides with the diameter of the circle, then R = AB / 2.

The right-angled triangle ABC is isosceles, AC = BC, then its acute angles are equal to 45.

Then Cos45 = AC / AB.

AB = AC / Cos45 = 4 / (√2 / 2) = 8 / √2 = 4 * √2 cm.

Then R = AB / 2 = 4 * √2 / 2 = 2 * √2 cm.

Answer: The radius of the circumscribed circle is 2 * √2 cm.

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