Question
Length of a chord in a circle of radius 'r' cm, is 24 cm
and distance between chord and centre of the circle is 35 cm. Find the value of (6r - 80).Solution
AB is the chord of circle.
Perpendicular line joining the centre of circle and chord, bisects the chord.
i.e. AC = BC = (24/2) = 12 cm
By Pythagoras theorem,
OA 2 = OC 2 + AC 2
Or, r 2 = 35 2 + 12 2
Or, r 2 = 1225 + 144
Or, r 2 = 1369
So, 'r' = 37
But length cannot be negative. So, 'r' = 37
Required value = 6 X 37 - 80 = 142
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