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0580 P23 - Jun 2026 - Q13 - 3 marks
10646
Circle centred at O with diameter AC and midpoint M of chord AB

\(A,B,C\) lie on a circle with centre O, and AOC is a straight line. M is the midpoint of AB. \(AB=6\text{ cm}\), \(OM=4\text{ cm}\).

(a) Find \(OA\). [2]

(b) Give a geometrical reason why \(\angle ABC=90^\circ\). [1]

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