Question

A chord AB of a circle of radius $10$cm makes a right angle at the centre of the circle. Find the area of the major and minor segments (Take $\pi =3.14$)

• A. Area of major segment$=285.5c{m}^2$, Area of minor segment$=28.5c{m}^2$
• B. Area of major segment$=232c{m}^2$, Area of minor segment$=24.6c{m}^2$
• C. Area of major segment$=212.7c{m}^2$, Area of minor segment$=32.5c{m}^2$
• D. Area of major segment$=196.2c{m}^2$, Area of minor segment$=21.3c{m}^2$

Answer 1

The correct option is A Area of major segment$=285.5c{m}^2$, Area of minor segment$=28.5c{m}^2$

Area of segment $APBA$ $=$ area of sector $OAPB-$area of $\Delta OAB$

$=\frac{\theta }{{360}^0}\times \pi r^2-\frac{1}{2}\times OB\times OA$

$=\frac{{90}^0}{{360}^0}\times \frac{22}{7}\times 10\times 10-\frac{1}{2}\times 10\times 10$

$=\frac{550}{7}-50=\frac{550-350}{7}=\frac{200}{7}$

$=28.5{cm}^2$

Area of major segment $=$ $\pi r^2-28.5=\frac{22}{7}\times 10\times 10-28.5$

$=$ $\frac{2200}{7}-28.5=\frac{2200-199.5}{7}=\frac{200.5}{7}$

$=$ $285.5$ ${cm}^2$