Question

A chord of length 6 cm is drawn in a circle of radius 5 cm. Calculate its distance from the centre 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.

     ∴ AC = CB = 3 cm
                In ΔOCA,
      OA2 = OC2 + AC2 (By Pythagoras theorem)
  ⟹ OC2 = (5)2 – (3)2 = 16
  ⟹ OC   = 4 cm