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9Â years, 1Â month ago
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?
8Â years, 7Â months ago
Let CE be the perpendicular on AD.
Now AC = 8^2 - 4 = rt60(Angle in a semi cirlce is right angle so we can use pythagoras theorem)
Now area of the triangle ACD = 1/2*2*rt60 = rt60 = 1/2*8*x => x = rt15/2
Now, In triangle EDC,
By pythagoras theorem ED^2 = 4 - 15/4 = .25
=> ED = .5
Thus BC = 8 - 2*.5= 7 cm
Hope that helps.
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