Chords are Equal!
AB and BC are two equal chords of a circle of length each. If the radius of the circle is , then enter the length of chord AC (in cm).
The answer is 8.
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1 solution
Given circle is x 2 + y 2 = 2 5
Choosing point ( 5 , 0 ) as B we need two equal chords AB and CB of length 2 5 . This can be done by drawing another circle of radius 2 5 centered at ( 5 , 0 )
The equation of this circle is ( x − 5 ) 2 + y 2 = 2 0
On solving the two equations for points of intersection we obtain points A and C as ( 3 , 4 ) and ( 3 , − 4 )
Therefore, the distance between the above two points is ( 3 − 3 ) 2 + ( − 4 − 4 ) 2 = 8