Question

Given inside a circle, whose radius is equal to 13 cm, is a point M at a distance 5 cm from the centre of the circle. A chord $AB=25$ cm is drawn through M The lengths of the segments into which the chord AB is divided by the point M in CM are

• A. 12, 13
• B. 14, 11
• C. 15, 10
• D. 16, 9

Answer 1

The correct option is D 16, 9

Draw a perpendicular OD from O to AB.
$\therefore$ $AD=\frac{25}{2}$ $=12.5$
In right angled $\Delta ODA$,
$O{A}^2=O{D}^2+A{D}^2$
$\left({13}^2\right)=O{D}^2+\left({12.5}^2\right)$
or $O{D}^2=169-156.25$
$=12.75$Again in right angled $\Delta ODM,$
$O{M}^2=O{D}^2+D{M}^2$
$5^2=12.75+D{M}^2$
$\therefore$ $D{M}^2=25-12.75=12.25$
$DM=\sqrt{12.25}=3.5cm$
$\therefore$ $AM=12.5+3.5=16cm$
and $MB=9cm$