Question

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.

• A. 2 cm
• B. $\sqrt{8}$ cm
• C. 4 cm
• D. $4\sqrt{2}$ cm

Answer 1

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,$PC=PD=\frac{CD}{2}$
From intersecting chords property,

$PA\times PB=P{C}^2$
2 x 4=$P{C}^2$
PC=$\sqrt{8}$
Therefore, $CD=2\times PC=2\times \sqrt{8}=4\sqrt{2}$ cm