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Question
In the figure given below, O is the centre of the circle. AB and CD are two chords of the circle. OM is perpendicular to AB and ON is perpendicular to CD.
AB = 24 cm, OM= 5 cm, ON= 12 cm. Find the:
1) radius of the circle
2) length of chord CD.
Solution
A line from centre to a chord that is perpendicular to it, bisects it.
It is given that AB = 24 cm
Thus, MB = 12 cm
1) Applying Pythagoras theorem for ΔOMB,
`OM^2 + MB^2 = OB^2`
`=> 5^2 + 12^2 = OB^2`
`=> OB = 13`
Thus, radius of the circle = 13 cm.
2) Similarly, applying Pythagoras theorem for ΔOND,
`ON^2 + ND^2 = OD^2`
OD is the radius of the circle
`=> 12^2 + ND^2 = 13^2`
`=> ND = 5`
A line from center to a chord that is perpendicular to it, bisects it.
ND = 5 cm
Thus, CD = 10 cm
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