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Standard X

Mathematics

Arc/Chord Properties of Circles

The radius OB...

Question

The radius OB of a circle is perpendicular to a chord PQ of length 12 cm. If the radius meets the chord at a point A, then the length of AP =.

4 cm

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5 cm

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6 cm

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Solution

The correct option is C 6 cm

From figure, it is clear that $O A ⊥ P Q .$
We know that the perpendicular drawn from the centre of circle to a chord bisects the chord.
$∴ A P = A Q = \frac{P Q}{2} = \frac{12}{2} c m = 6 cm .$

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The radius OB of a circle is perpendicular to a chord PQ of length 12 cm. If the radius meets the chord at a point A, then the length of AP =.

The correct option is C 6 cm From figure, it is clear that OA⊥PQ. We know that the perpendicular drawn from the centre of circle to a chord bisects the chord. ∴AP=AQ=PQ2=122cm=6 cm.

The correct option is C 6 cm

From figure, it is clear that $O A ⊥ P Q .$
We know that the perpendicular drawn from the centre of circle to a chord bisects the chord.
$∴ A P = A Q = \frac{P Q}{2} = \frac{12}{2} c m = 6 cm .$