Question

In a circle of radius 10 cm, AB and CD are two parallel chords of lengths 16 cm and 12 cm respectively.
Calculate the distance between the chords, if they are on:
(i) the same side of the center.
(ii) the opposite sides of the center.

Answer 1

Given that AB = 16 cm and CD = 12 cm
So, AL = 8 cm and CM = 6 cm   ....( ⊥ from the center to the chord bisects the chord )

In right triangle OLA and OMC,
By Pythagoras theorem,
OA² = OL² + AL² and OC² = OM² + Cm² 
10² = OL² + 8² and 10² = OM² + 6²
OL² = 100 - 64 and OM² = 64
OL² = 6 cm and OM² = 8 cm

(i) In the first case, distance between AB and CD is
LM= OM - OL = 8 - 6 = 2 cm

(ii) In the second case , distance between AB and CD is
LM = OM + OL = 8 + 6 = 14 cm