ICSE Class X Math 2014 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 $C D$ .

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

Question : 49 of 52

Marks: +1, -0

radius of the circle.

Solution:

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

\; \text{cm} .

\because OM \perp AB

M

is mid point of

A B

\therefore AM=12 \text{cm} .

Let radius of circle

=r

From

\triangle

AMO;

AO^2=AM^2+OM^2

(By Pythagoras theorem)

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

\;=144+25=169

r\;=13 \text{cm} .

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