Question

A chord is 8 cm away from the centre of a circle of radius 17 cm. Find the length of the chord.

Answer 1

Let AB be the chord with distance from the center $=8$ cm

$OA=radius=17cm$

Now, $OC\perp AB$

Then, $AC=CB=\frac{AB}{2}$.......$\left(i\right)$....(perpendicular drawn from the centre of the circle to the chord bisects the chord)

Now, $△ACO$ is right angled triangle at $C$

$\therefore AC=\sqrt{(O{A}^2-O{C}^2)}=\sqrt{({17}^2-8^2)}=\sqrt{\left(225\right)}=15cm$

Hence, $AB=2\times 15=30cm$ ............ From $\left(i\right)$