Question

find the length of a chord which is at a distance of 12 cm from the center of circle of radius 13 cm

Answer 1

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!!