Cut sector

Geometry Level 2

$\Gamma$ is a circle with center $O$ . $AOB$ is a circular sector of $\Gamma$ with $\angle AOB = 50^\circ$ . $C$ is a point on minor arc $AB$ such that $\angle AOC = 20 ^\circ$ . What is the measure (in degrees) of $\angle ACB$ ?

The answer is 155.

1 solution

Arron Kau Staff
May 13, 2014

Let $D$ be any point on the major arc of $AB$ . Then, $\angle ADB = \frac{1}{2} \angle AOB = 25^\circ$ .

Since $ACBD$ is a cyclic quadrilaterial, hence $\angle ACB = 180^\circ - \angle ADB = 155 ^\circ$ .

Note: The angle measure of $\angle AOC$ is irrelevant to the question.

Cut sector

The answer is 155.

1 solution

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