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In the Adjoining Figure, Point O is the Centre of the Cirlcle, Seg Om ⊥ Chord Ab. If Om = 8cm, Ab = 12 Cm, Then Find Ob. - Geometry

In the adjoining figure, point O is the centre of the cirlcle, seg OM ⊥ chord AB. If OM = 8cm, AB = 12 cm, then find OB.

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Solution

MB = 12 × AB = 12 × 12 = 6 cm (perpendicular drawn from the centre of the circle to the chord bisects the chord)
`OB^ = OM^2 + MB^2`              .....................(Pythagoras thearem)
= `8^2 + 6^2`
= 64 + 36 = 100
∴ OB = 10 cm

Concept: Angle Subtended by the Arc to the Point on the Circle
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