Question

In the given figure, $O$ is the centre of the circle $OB=5\text{cm}$. Distance from $O$ to chord $AB$ is $3\text{cm}$. Find the length of $AB$.

Answer 1

Radius of given circle $=OB=OA=5\text{cm}$

$OP=3\text{cm}$

If a perpendicular is dropped from center of the circle on a chord, it bisects the chord.

$⟹AB=2AP$

In right angles triangle $OAP$, using pythagoras theorem:

$AP=\sqrt{O{A}^2-O{P}^2}$

$AP=\sqrt{5^2-3^2}=4\text{cm}$

$AB=2\times 4\text{cm}=8\text{cm}$