Question

The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre?

Answer 1

Let AB and CD be two parallel chords in a circle centered at O. Join OB and OD. Distance of smaller chord AB from the centre of the circle = 4 cm OM = 4 cm

MB = AB/2 = 6/2 = 3cm

In ΔOMB,

OM² + MB² = OB²

(4)² + (3)² = OB²

16 + 9 = OB²

OB = 25

OB= 5cm

In ΔOND,

OD = OB = 5cm

ND = CD/2 = 8/2  = 4cm

ON² + ND² = OD²

ON² + (4)² = (5)²

ON² = 25 - 16 = 9

ON = 3

Therefore, the distance of the bigger chord from the centre is 3 cm.