Question

Choose the correct answer from the alternatives given :
In the given figure, O is the centre of the circle find $\angle CBD$.

• A. 140${}^{\circ }$
• B. 50${}^{\circ }$
• C. 40${}^{\circ }$
• D. 130${}^{\circ }$

Answer 1

The correct option is B 50${}^{\circ }$

$\angle APC=\frac{1}{2}\times \angle AOC=\frac{1}{2}\times 100={50}^{\circ }$
[Angle at circumference is half of the angle at centre.]
$\angle CBD=\angle APC={50}^{\circ }$ (alternate segment theorem).