In a circle of radius 10 cm, PQ and RS are two parallel chords of lengths 16 cm and 12 cm, respectively. What is the distance between the chords if they are on opposite sides of the centre?
Answer & explanation
Correct answer: option 3
We know that,
In this figure,
AC2 = AB2 + BC2
OP2 = OA2 + AP2
We have,
Radius = 10 cm
PQ = 16 cm
RS = 12 cm
In ΔOAP, = (10)2 = OA2 + (8)2
= OA2 = 100 – 64 = 36
= OA = 6 cm
In ΔOBR,
= (10)2 = OB2 + (6)2
= OB2 = 100 – 36 = 64
= OB = 8 cm
Now, AB = OA + OB = 6 + 8 = 14 cm