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

Let AB be the chord and O be the centre of the circle.
Let OC be the perpendicular drawn from O to AB.

We know, that the perpendicular to a chord, from the centre of a circle, bisects the chord.
∴ AC = CB
In ∆OCA,
OA² = OC² + AC²  (By Pythagoras theorem)
⇒ AC² = (17)² - (8)² = 225
⇒ AC = 51 cm
∴ AB = 2 AC = 2 × 15 = 30 cm