Question

A chord of length 8 cm is drawn at a distance of 3 cm from the centre of a circle. Calculate the radius of the circle.

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.
∴ 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 of the circle is 5 cm.