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gurpreetsingh
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Coordinate Geometry Approach:

BC = two times the x coordinate of the intersection of 2 circles y^2 = 16 - x^2 and y^2 = 4- (x-4)^2
Therefore solve for x: 16 - x^2 = 4 - (x-4)^2
x=7/2
BC = 2* (7/2) = 7
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gurpreetsingh
On a semicircle with diameter AD , chord BC is parallel to AD. Further each of the chords AB and CD has length 2.
Given AD = 8 , what is BC?

a) 7.5
b) 7
c) 7.75
d) 7.25
e) None of the above.

Do not have OA, open for discussion.

Please see the solution in image

IMO B
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gurpreetsingh
On a semicircle with diameter AD , chord BC is parallel to AD. Further each of the chords AB and CD has length 2.
Given AD = 8 , what is BC?

a) 7.5
b) 7
c) 7.75
d) 7.25
e) None of the above.

Do not have OA, open for discussion.

Co-ordinate Geometry Approach: -

\(x^2 + y^2 = 16\)

Let C have coordinates (x,y)
\((4-x)^2 + y^2 = 2^2 = 4\)
\(16 + x^2 - 8x + y^2 = 4\)
8x = 12 + 16 = 28
\(x = \frac{28}{8} = 3.5\)

Then B will have x = -3.5
BC = 2 * 3.5 = 7 since BC ||AD y coordinate will be same for B & C

IMO B
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