Question

Find the length of a chord which is at a distance of 5 cm from the centre of a circle of radius 10 cm. [use $\sqrt{75}=8.66$]

• A. 17 cm
• B. 17.32 cm
• C. 18.46 cm
• D. 19 cm

Answer 1

The correct option is B 17.32 cm

Distance of the chord from the centre = 5 cm (Given)
Radius of the circle = OA = 10 cm (Given)

In $△OCA$
Using Pythagoras' theorem,

$O{A}^2=A{C}^2+O{C}^2$
$100=A{C}^2+25$
$A{C}^2=100-25=75$
$AC=\sqrt{75}=8.66$

As, perpendicular from the centre to the chord bisects the chord,
Therefore , AC = BC = 8.66 cm
$\Rightarrow AB=AC+BC=8.66+8.66=17.32$