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?
Explanation:
Quadrilateral ABCD is an isosceles trapezium. Let AM = DN = x
∵ 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).
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