Question

The radius of a circle is $17.0$ cm and the length of perpendicular drawn from its centre to a chord is $8.0$ cm. Calculate the length of the chord.

Answer 1

In the figure, $AC$ is the chord and $OB$ is a perpendicular drawn from the center $O$ on the chord.

Radius of the circle, $r=OC=17$ cm

Perpendicular length, $OB=8$ cm

Now triangle $OBC$ is a right-angled triangle.

From Pythagoras theorem,

$B{C}^2=O{C}^2-O{B}^2$

$={17}^2-8^2$

$=289-64$

$=225$

$BC=\sqrt{225}=15$ cm

Theorem: Perpendicular drawn from the center of a circle to the chord, bisects the chord.

So, length of the chord $AC=2BC=30$ cm