Question

In the above figure O is the center of the circle $\angle$AOB $={80}^{\circ },$ ^,then complete the matching.

$\begin{array}{cc}\text{Angle}& \text{Value}\\ 1.ACB& a.90\\ 2.ADB& b.40\\ 3.ABC& c.80\\ 4.AOC& d.180\end{array}$

• A. a-1, b-2, c-3, d-4
• B. a-2, b-1, c-3, d-4
• C. a-4, b-3, c-2, d-1
• D. a-3, b-2, c-2, d-1

Answer 1

The correct option is C

a-4, b-3, c-2, d-1

AOC is a straight line, so $\angle$AOC should be a straight angle. Therefore $\angle$AOC $={180}^{\circ }$.

Diameter is also a chord of the circle. The angle subtended by AC at the center is $\angle$AOC $={180}^{\circ }$

Since, angle subtended by a chord at the center is equal to twice the angle subtended by chord at any point on the circle,

We get, $\angle$AOC $=2\angle$ABC

$\Rightarrow \angle$ABC $={90}^{\circ }$

Similarly, $\angle$ADB $=\frac{1}{2}\angle$AOB

$\Rightarrow \angle$ACB $=\frac{1}{2}\angle$AOB

From the above equations we can see that $\angle$ADB $=\angle$ACB $=\frac{1}{2}\angle$AOB

$\Rightarrow \angle$ADB $=\angle$ACB $={40}^{\circ }$