Question
Length of a chord in a circle of radius 'r' cm, is 14 cm
and distance between chord and centre of the circle is 24 cm. Find the value of (4r - 60).Solution
AB is the chord of circle.
Perpendicular line joining the centre of circle and chord, bisects the chord.
i.e. AC = BC = (14/2) = 7 cm
By Pythagoras theorem,
OA 2 = OC 2 + AC 2
Or, r 2 = 24 2 + 7 2
Or, r 2 = 576 + 49
Or, r 2 = 625
So, 'r' = 25
But length cannot be negative. So, 'r' = 25
Required value = 4 X 25 - 60 = 40
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