Question
Length of a chord in a circle of radius 'r' cm, is 18 cm and distance between chord and centre of the circle is 40
cm. Find the value of (3r + 7).
Solution
AB is the chord of circle.
Perpendicular line joining the centre of circle and chord, bisects the chord.
i.e. AC = BC = (18/2) = 9 cm
By Pythagoras theorem,
OA 2 = OC 2 + AC 2
Or, r 2 = 40 2 + 9 2
Or, r 2 = 1600 + 81
Or, r 2 = 1681
So, 'r' = 41
But length cannot be negative. So, 'r' = 41
Required value = 3 X 41 + 7 = 130
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