Question

A chord of length 6 cm is drawn in a circle of radius 5 cm.

Calculate its distance from the center of the circle.

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 = 3 cm

In ΔOCA,

OA² = OC² + AC²                    ...( By Pythagoras theorem )

⇒ OC² = (5)² - (3)²

⇒ OC = 16 

⇒ OC = 4 cm