Question
Length of a chord in a circle of radius 'r' cm, is 40 cm
and distance between chord and centre of the circle is 21 cm. Find the value of (2r + 1).Solution
AB is the chord of circle.
Perpendicular line joining the centre of circle and chord, bisects the chord.
i.e. AC = BC = (40/2) = 20 cm
By Pythagoras theorem,
OA 2 = OC 2 + AC 2
Or, r 2 = 21 2 + 20 2
Or, r 2 = 441 + 400
Or, r 2 = 841
So, 'r' = 29
But length cannot be negative. So, 'r' = 29
Required value = 2 X 29 + 1 = 59
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