find the length of a chord which is at a distance of 12 cm from the centre of the circle of radius 13 cm
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Answer: 10 cm
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AB is chord of a circle with center O and OA is its radius OM ⊥ AB
Therefore, OA = 13 cm, OM = 12 cm
Now from right angled triangle OAM,
OA2 = OM2 + AM2 by using Pythagoras theorem,
132 = 122 + AM2
AM2 = 132 – 122
AM2 = 169 – 144
AM2 = 25
AM = 52
We know that OM perpendicular to AB
Therefore, M is the midpoint of AB
AB = 2 AM
AB = 2 (5)
AB = 10 cm
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