Question

If the diameter of this circle is 10 cm, find the length of the chord AB.

Answer 1

$AB$, a line segment forms a chord in this circle that intersects the circle at $2$ points and is a part of a secant line. Let O be the centre of the circle.

Diameter of the circle $d=10cm$
$\therefore$ Radius of the circle $=\frac{d}{2}=\frac{10}{2}=5cm$


We can utilise the Pythagoras Theorem to determine the length of the chord.

$A{B}^2=O{A}^2+O{B}^2$
Since $OA$ and $OD$ are the radius of a circle, $OA=OB=5cm$
$⟹A{B}^2=5^2+5^2$
$=25+25$
$=50cm$
$⟹AB=\sqrt[2]{250}=7.07cm$