Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 3.6 AMC 10/12 Find the answer Italy

Problem:

Let $ABC$ be an isosceles triangle such that $\angle BAC = 120^\circ$ and $AB = AC = 1$ . What is the radius of the circumscribed circle?

Pick one

Solution

Solution:

The answer is (D). Let us call $O$ the center of the circumscribed circle and consider the triangle $AOC$ . It is isosceles at $O$ and, on the other hand, $\angle AOC = \frac{1}{2} \angle BAC = 60^\circ$ ; hence $AOC$ is equilateral.

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Source: MathNet, licensed CC-BY-4.0. Statement translated into English from it; metadata (topic, difficulty) added by this project.