Question

In a circle, the major arc is 3 times the minor arc. The corresponding centre angles and the degree measures of two arcs are

• A. ${90}^{o}and{270}^o$
• B. ${90}^{o}and{90}^o$
• C. ${270}^{o}and{90}^o$
• D. ${60}^{o}and{210}^o$

Answer 1

The correct option is C

${270}^{o}and{90}^o$

In a circle, major arc is 3 times the minor arc i.e. arc ACB = 3 arc ADB.

$\therefore Reflex\angle AOB=3\angle AOB$

Let $\angle AOB=x$

Then reflex $\angle AOB=3x$

But angle at $O={360}^o$

$\therefore x+3x={360}^o$

$\Rightarrow 4x={360}^o$

$\Rightarrow x=\frac{{360}^o}{4}={90}^o$

$\therefore 3x={90}^o\times 3={270}^o$

Hence, angles are ${270}^{o}and{90}^o$.