CAT 2004 — QA Question 21
Basics of CirclesEasy
On a semicircle with diameter AD, chord BC is parallel to the diameter. Further, each of the chords AB and CD has length 2, while AD has length 8. What is the length of BC?
Answer & solution
Correct answer: 7
- A
7.5
7
- C
7.75
- D
None of the above
Solution
Quadrilateral ABCD is an isosceles trapezium. Let AM = DN = x
âµ AD = 8, AO = DO = BO = 4
∴ OM = ON = 4 – x
ΔBMO and ΔBMA are right triangles.
∴ OB2 = OM2 + MB2
∴ 16 = (4 – x)2 + h2 …(i)
Also,
AB2 = MB2 + AM2
4 = x2 + h2 …(ii)
From (i) and (ii), x = 0.5
∴ BC = 2(4 – x)
∴ BC = 7
Hence, option (b).