Question

In the adjoining figure, O is the centre of the circle whose radius is MN. Measures of some central angles are given. If the measure of the Arc AB is 'a' units and that of Arc CD is 'b' units, then which of the following options is correct.

• A. a = b
• B. a > b
• C. a < b
• D. None of the above

Answer 1

The correct option is A a = b

Given, MN is the diameter of the circle.
Hence, $\angle MOA+\angle AOB+\angle BON={180}^{\circ }$
$\Rightarrow {80}^{\circ }+\angle AOB+{20}^{\circ }={180}^{\circ }$
$\Rightarrow \angle AOB={80}^{\circ }$.

Similarly, the measure of $\angle COD={80}^{\circ }$.

Since, $\angle AOB=\angle COD$,
so, the measure of Arc AB = the measure of Arc CD.
Hence, a = b.