Question
Length of a chord in a circle of radius 'r' cm, is 16 cm
and distance between chord and centre of the circle is 15 cm. Find the value of (5r - 19).Solution
AB is the chord of circle.
Perpendicular line joining the centre of circle and chord, bisects the chord.
i.e. AC = BC = (16/2) = 8 cm
By Pythagoras theorem,
OA 2 = OC 2 + AC 2
Or, r 2 = 15 2 + 8 2
Or, r 2 = 225 + 64
Or, r 2 = 289
So, 'r' = 17
But length cannot be negative. So, 'r' = 17
Required value = 5 X 17 - 19 = 66
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