Question

Two chords AB and CD of lengths 5 cm 11cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6 cm, find the radius of the circle.

Answer 1

Draw OM ⊥ AB and ON ⊥ CD. Join OB and OD.

(Perpendicular from the centre bisects the chord)

Let ON be x. Therefore, OM will be 6− x.

In ΔMOB,

In ΔNOD,

We have OB = OD (Radii of the same circle)

Therefore, from equation (1) and (2),

From equation (2),

Therefore, the radius of the circle iscm.