Question

The centre of a circle is at $O$. $AB$ and $CD$ are two chords of length $d$ and $l$ respectively. If $P$ is the mid point of $CD$, then the length $OP$ is

• A. $\sqrt{d^2+l^2}$
• B. $\sqrt{d^2-l^2}$
• C. $\frac{1}{2}\sqrt{d^2+l^2}$
• D. $\frac{1}{2}\sqrt{d^2-l^2}$

Answer 1

The correct option is D $\frac{1}{2}\sqrt{d^2-l^2}$

$O{P}^2={\left(\frac{d}{2}\right)}^2-{\left(\frac{l}{2}\right)}^2=\frac{d^2}{4}-\frac{l^2}{4}=\frac{d^2-l^2}{4}$
$OP=\frac{\sqrt{d^2-l^2}}{2}$