Two parallel chords on the same side of the centre of a circle are 12 cm and 20 cm long and the radius of the circle is 5√13 cm. What is the distance (in cm) between the chords?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is 3 i.e. 2.
Length of the chords: RS = 12 cm, PQ = 20 cm
Radius = 5√13 cm
Lenghth of VS = RS/2 = 6 cm
Length of TQ = PQ/2 = 10 cm [Radius divides the chords in 2 equal parts]
In ΔOVS using the pythagoras theorem:
OS2 = OV2 + US2
⇒ (5√13)² = OV² + 6²
⇒ OV = √289 = 17 cm
In ΔOTR using the pythagoras theorem:
OQ2 = OT2 + TQ2
⇒ (5√13)2 = OT2 + 102
⇒ OT2 = 325 - 100 = 225
⇒ OT = √225 = 15 cm
Hence,
Distance between chords = OV - OT = 17 - 15 = 2 cm