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?

Hi Hriday,

let us drop perpendiculars from B and C on to AD and name them as E,F.

ACD is a right triangle,CD =2 and AD = 8

Hence, AC = (60)^(0.5)

let us find the the height of ACD which is CF by equating the areas of ACD found by taking AC and AD as bases

we get CF =Sqrt(15)/2 

from that we ED from the right riangle CFD

We get ED = 0.5

BC = AD-2(0.5) = 7

Hope that helps.

Thanks,

Varun.