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A Line through the Center That Bisects the Chord Is Perpendicular to the Chord.

In the figure...

Question

In the figure, seg OM ⊥ chord AB and l (AM) = 1.5 cm.
Find the length of seg BM and seg AB.

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Solution

For the given circle, seg OM ⊥ AB; l(AM)= 1.5 cm
Seg AM = seg BM (Perpendicular drawn from the centre to a chord bisects the chord)
So, seg MB = 1.5 cm
Seg AB = Seg AM + Seg MB
= 1.5 cm + 1.5 cm = 3cm
∴ Seg MB = 1.5 cm
And seg AB = 3 cm

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