Question

Calculate the length of a chord which is at a distance of $12\text{cm}$ from the center of a circle of radius $13\text{cm}$

Answer 1

From figure,

$AB$ is the length of the chord,

and $AC=BC$ (perpendicular from the center to the chord bisects the chord)

Using Pythagoras theorem in $△AOC$

$⟹A{O}^2=A{C}^2+O{C}^2$

$⟹{13}^2=A{C}^2+{12}^2$

$⟹A{C}^2=169-144$

$⟹A{C}^2=25$

$⟹AC=5$

Hence, $AB=AC+BC$

$⟹AB=5+5$

So, length of chord $AB=10\text{cm}$