Question

A chord of length 8 cm is drawn at a distance of 3 cm from the center of the circle.
Calculate the radius 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.
∴ AB = 8 cm
⇒ AC = CB = `"AB"/2`

⇒ AC = CB = `8/2`

⇒ AC = CB =  4 cm

In OCA,
OA² = OC² + AC²            ...( By Pythagoras theorem )
⇒ OA² = ( 4 )² + ( 3 )² = 25
⇒ OA = 5 cm

Hence, radius oof the circle is 5 cm.