Question

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

Answer 1

Let AB be the chord and O be the center of the circle.

Let OC be the perpendicular drawn from O to AB.

We know, that the perpendicular to a chord, from the center of a circle, bisects the chord.

∴ AC = CB

In ΔOCA,
OA² = OC² + AC²                       ...( By Pythagoras theorem )

⇒ AC² = (17)² - (8)² = 225

⇒ Ac = 15 cm

∴ AB = 2 AC = 2 x 15 = 30 cm.