A corner shop's circular wall clock has centre \(O\), with \(OA\) a radius drawn to the edge and \(AB\) a straight support bracket tangent to the clock face...
Question 1 Report
A corner shop's circular wall clock has centre \(O\), with \(OA\) a radius drawn to the edge and \(AB\) a straight support bracket tangent to the clock face at \(A\), as shown. Given angle \(OBA = 25^{\circ}\), write down the size of angle \(OAB\), giving a reason, and hence find angle \(AOB\). (2)
Answer Details
A tangent to a circle is always perpendicular to the radius drawn to the point of contact, so angle \(OAB = 90^{\circ}\), because \(AB\) is tangent to the clock face at \(A\) and \(OA\) is the radius there. [1 mark]
The three angles of triangle \(OAB\) sum to \(180^{\circ}\), so angle \(AOB = 180-90-25 = 65^{\circ}\). [1 mark]
This tangent-radius right angle is a fact worth quoting explicitly as the reason, since the question specifically asks for one.
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