find the length of a chord which is at a distance of 12 cm from the center of circle of radius 13 cm
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Hey mate.
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Let, P be the mid point of AB, So
'.' AP = PB
OP = 12 cm = distance of chord from center
And,
AO = 13 cm = Radius
Now, OPA forms a right angle triangle.
Now, by pythagoras theorem,
AO^2 = OP^2 + AP^2
AP^2 = AO^2 - OP^2
AP^2 = 13^2 - 12^2
AP^2 = 169 - 144
AP^2 = 25
AP = 5 cm.
Now,
AB = AP + PB = AP + AP = 5 +5 = 10 cm.
Thus,
The length of the chord is 10 cm
Hope it helps!!
========
Let, P be the mid point of AB, So
'.' AP = PB
OP = 12 cm = distance of chord from center
And,
AO = 13 cm = Radius
Now, OPA forms a right angle triangle.
Now, by pythagoras theorem,
AO^2 = OP^2 + AP^2
AP^2 = AO^2 - OP^2
AP^2 = 13^2 - 12^2
AP^2 = 169 - 144
AP^2 = 25
AP = 5 cm.
Now,
AB = AP + PB = AP + AP = 5 +5 = 10 cm.
Thus,
The length of the chord is 10 cm
Hope it helps!!
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