Question

In adjoining figure $AB$ is a chord of a circle and $\angle ADB={45}^o,\angle ACB$ will be:

• A. ${45}^o$
• B. ${60}^o$
• C. ${90}^o$
• D. ${135}^o$

Answer 1

The correct option is A ${45}^o$

As shown the figure chord AB make divides the circle into two segments, one is major and another one is a minor segment.

We know, that the angle made by a chord of the circle at the centre of the circle is double the angle made by the chord at any point on the circumference of the circle lying on the same side of it.

$\therefore \angle AOB=\frac{1}{2}\angle ADB=\frac{1}{2}\angle ACD$

$\Rightarrow \angle ACD=\angle ADB={45}^o$