CAT 2005 — QA Question 9
Answer the next 2 questions based on the information given below.
Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.
What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm?
Answer & solution
- A
1 or 7
- B
2 or 14
- C
3 or 21
4 or 28
The two chords AB and CD can be on the same side or the opposite sides of the centre O.
Let M and N be the midpoints of AB and CD.
∴ MN is the distance between the two chords.
MB = 12 cm and ND = 16 cm
OM and ON are perpendicular to AB and CD respectively.
ON2 = OD2 - ND2 (By Pythagoras theorem)
⇒ ON2 = 202 – 162 âââââââ
⇒ ON = 12 cm
Similarly,OM2 = OB2 - MB2
⇒ OM = 16 cm
Case 1: AB and BC are on the same side of the centre.
MN = OM – ON = 4 cm
Case 2: AB and BC are on opposite sides of the centre.
MN = OM + ON = 28 cm
Hence, option (d).