Question

In the given figure, radius of the circle is \(5~cm\) and perpendicular distance from the centre of the circle to the chord \(AC\) is \(3~cm\).
Find the length of the chord \(AC\).

Answer 1

In $△OAB$, applying Pythagoras Theorem:

$O{A}^2=O{B}^2+A{B}^2$

$\Rightarrow 5^2=3^2+A{B}^2$

$\Rightarrow A{B}^2=5^2-3^2=25-9=16$

$\Rightarrow AB=\sqrt{16}=4cm$

We know that perpendicular from the centre of the circle to the chord, bisects the chord.

$\Rightarrow AB=BC$

Now, $AC=AB+BC$

$\Rightarrow AC=AB+AB=2AB$ [$\because AB=BC$]

$\Rightarrow AC=2\times 4=8cm$