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Question
The radius of a circle is 6 cm. The perpendicular distance from the centre of the circle to the chord which is 8 cm in length, is
Options
- \[\sqrt{5} \] cm
- \[2\sqrt{5}\] cm
\[2\sqrt{7} \] cm
- \[\sqrt{7}\] cm
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Solution
We will represent the given data in the figure
We know that perpendicular drawn from the centre to the chord divides the chord into two equal parts.
So , AM = MB = \[\frac{AB}{2} = \frac{8}{2}\] = 4 cm.
Using Pythagoras theorem in the ΔAMO,
`OM^2 = AO^2 - AM^2`
`= 6^2 - 4^2`
= 36-16
`= sqrt(20)`
= `2sqrt(5)` cm
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