Question

The lengths of parallel chords which are on opposite sides of the centre of a circle are 6 cm and 8 cm. If radius of the circle is 5 cm, then the distance between these chords is _____. 

(A) 2 cm 

(B) 1 cm 

(C) 8 cm 

(D) 7 cm

Answer 1

PQ = 8 cm, MN = 6 cm 

∴ AQ = 4 cm, BN = 3 cm 

∴ OQ² = OA² + AQ² 

∴ 5² = OA² + 4² 

∴ OA² = 25 – 16 = 9 

∴ OA = 3 cm 

Also, ON² = OB² + BN² 

∴ 5² = OB² + 3² 

∴ OB = 4 cm 

Now, AB = OA + OB = 3 + 4 = 7 cm