Question

A chord of a circle of radius $7$ cm. subtends an angle of ${90}^o$ at its centre. The ratio of areas of smaller and larger segment is

• A. $2:7$
• B. $1:10$
• C. $1:11$
• D. none of these

Answer 1

The correct option is B $1:10$

Area smaller segment

= ar sector $OAPB-$ar$\Delta$$OAB$

= $\frac{{90}^0}{{360}^0}\times \frac{22}{7}\times 7\times 7-\frac{1}{2}\times 7\times 7$

= $\frac{77}{2}-\frac{49}{2}=\frac{28}{7}=14{cm}^2$

Area of largere segment $=$ ar of circle - $14$

$=$ $\pi r^2-14=\frac{22}{7}\times 7\times 7-14$

$=$ $154-14$

$=$ $140$ ${cm}^2$

Therefore required ratio $=$ $14:140$=$1:10$