The radius of the circle is 13 cm and AB is chord which is at a distance of 12 cm from the center. Then the length of the chord is A. 16 cm B. 10 cm C. 8 cm D. 15 cm
Let O be the center of Circle and AB be the chord.
P be the midpoint of AB, So
AP = PB
OP = 12 cm = distance of chord from center
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.
AB = AP + PB = AP + AP = 5 +5 = 10 cm.