Question

Given, inside a circle whose radius is equal to 13 cm, M is a point at a distance 5 cm from the centre of the circle. A chord $AB=25cm$ is drawn through M. The lengths of the segments into which the chord AB is divided by the point M 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 angle $△ODA$
$O{A}^2=O{D}^2+A{D}^2$
$(13{)}^2=O{D}^2+(12.5{)}^2$
or, $O{D}^2=169-156.25=12.75$
Again, in right angle $△ODM$
$O{M}^2=O{D}^2+D{M}^2$
$5^2=12.75+D{M}^2$
$\therefore D{M}^2=25-12.75=12.25$
$DM=\sqrt{12.25}=3.5cm$
$\therefore AM=12.5+3.5=16cm$
and $MB=9cm$