Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 2.3 Junior Find the answer

A circle of radius $10$ inches has its center at the vertex $C$ of an equilateral triangle $ABC$ and
passes through the other two vertices. The side $AC$ extended through $C$ intersects the circle
at $D$ . The number of degrees of angle $ADB$ is:

Pick one

Solution

$ABC$ is an equilateral triangle, so ∠ $C$ must be $60$ °. Since $D$ is on the circle and ∠ $ADB$ contains arc $AB$ , we know that ∠ $D$ is $30$ ° $\implies \fbox{B}$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.