AB is the diameter of a circle with centre O. CD is a chord perpendicular to diameter intersecting it at P. Find the length of chord if PA = 2 cm and PB = 4 cm.

2 cm

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$\sqrt{8}$ cm

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4 cm

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$4 \sqrt{2}$ cm

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Solution

The correct option is D
$4 \sqrt{2}$ cm

We know that chord of a circle is bisected by the diameter which is perpendicular to it.
Therefore, $P C = P D = \frac{C D}{2}$
From intersecting chords property,

$P A \times P B = P C^{2}$
2 x 4= $P C^{2}$
PC= $\sqrt{8}$
Therefore, $C D = 2 \times P C = 2 \times \sqrt{8} = 4 \sqrt{2}$ cm

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AB is the diameter of a circle with centre O. CD is a chord perpendicular to diameter intersecting it at P. Find the length of chord if PA = 2 cm and PB = 4 cm.

The correct option is D 4√2 cm We know that chord of a circle is bisected by the diameter which is perpendicular to it. Therefore,PC=PD=CD2 From intersecting chords property, PA×PB=PC2 2 x 4=PC2 PC=√8 Therefore, CD=2×PC=2×√8=4√2 cm