ICSE Class X Math 2014 Solved Paper

In the figure given below, $O$ is the centre of the circle. $A B$ and $C D$ are two chords of the circle. $O M$ is perpendicular to $A B$ and $O N$ is perpendicular to $C D$ .

$A B=24 {\cm}, O M=5 {\cm}, O N=12 {\cm} . \;\text " Find "\;$ the :

Question : 49 of 52

Marks: +1, -0

radius of the circle.

Solution:

\;\;\text " Given : "\; {\AB}=24 {\cm} ; {\OM}=5 {\cm}, {\ON}=12

\; {\cm} .

∵ {\OM} \⟂ {\AB}

M

is mid point of

A B

∴ {\AM}=12 {\cm} .

Let radius of circle

=r

From

△

AMO;

{\AO}^2= {\AM}^2+ {\OM}^2

(By Pythagoras theorem)

r^2\;=(12)^2+(5)^2

\;=144+25=169

r\;=13 {\cm} .

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