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Geometry Difficulty 1.3 Junior Find the answer Canada

In the diagram, a semi-circle has centre $O$ and diameter $AC$ . Also, $B$ is a point on the circumference such that $\angle BAC = 25\degree$ .The measure of $\angle BOC$ is

Pick one

Solution

Since $O$ is the centre of the circle, then $OA = OB = OC$ . This means that $\triangle AOB$ and $\triangle COB$ are both isosceles with $\$\angle$ ABO = $\angle$ BAO = $\angle$ BAC =
$25\degree$ $. Thus,$ $\angle$ AOB = $180\degree - \angle$ ABO -
$\angle$ BAO = $130\degree$ $. Since$ $\angle$ AOC $is a straight angle, then$ $\angle$ BOC = $180\degree - \angle$
AOB = $180\degree - 130\degree = 50\degree\$.$

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