Question

The radius of a circle is 13 cm and the length of one of its chord is 10 cm. Find the distance of the chord from the centre.

Answer 1

Let AB be a chord of a circle with centre O and radius 13cm such that AB = 10 cm.
From O, draw OL ⊥ AB. Join OA.
Since, the perpendicular from the centre of a circle to a chord bisects the chord.
∴ AL = LB = `1/2`AB = 5 cm.

Now, in right triangle OLA, we have
OA² = OL² + AL²
⇒ 13² = OL² + 5²
⇒ 13² - 5² = OL²
⇒ OL² = 144
⇒ OL = 12 cm
Hence, the distance of the chord from the centre is 12 cm.