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Question
If the length of a chord of a circle is 16 cm and is at a distance of 15 cm from the centre of the circle, then the radius of the circle is
Options
15 cm
16 cm
17 cm
34 cm
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Solution
17 cm
We will represent the given data in the figure
In the diagram AB is the given chord of 16 cm length and OM is the perpendicular distance from the centre to AB.
We know that perpendicular from the centre to any chord divides it into two equal parts.
So, AM = MB = `16/2` = 8 cm.
Now consider right triangle OMA and by using Pythagoras theorem
`AO^2 = AM^2 + OM^2`
`= 8^2 + 15^2`
= 64+225
= 289
`= sqrt(289)`
= 17 cm
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