Chords
Geometry
Level
3
Two parallel chords in a circle have lengths 6 and 8. The distance between them is 1. Find the diameter of the circle.
The answer is 10.
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We will apply pythagoras for 2 sets, let the perpendicular between centre and big chord be x, and center and small chird be x+1. Since perpendicular bisects the chord, we have 2 pythagorean triplets i.e ( x , 4 , r ) and ( x + 1 , 3 , r ). Solving x 2 + 1 6 = ( x + 1 ) 2 + 9 = r 2 , we get x = 3 a n d r = 5 . Thus answer is 10