Circle Geometry, SMB-009

In the diagram, \(OB\) meets the chord \(AC\) such that \(AB = BC\).

The length of chord \(AC = 24\), and \(OC = 13\).

Find the length of \(OB\). (3 marks)

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\(OB=5\)

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\(OB \perp AC\ \ \text{(line through centre that bisects chord)}\)

\(BC= \dfrac{1}{2} \times 24 = 12 \)

\(\text{Using Pythagoras in}\ \Delta OBC :\)