CAT 2017 Set-2 | Question: 84

Question

$\text{ABCD}$ is a quadrilateral inscribed in a circle with centre $\text{O}$. If $\angle \text{COD} =120$ degrees and $\angle \text{BAC} = 30$ degrees, then the value of $\angle \text{BCD}$ (in degrees) is

• A. $89$
• B. $87$
• C. $86$
• D. $90$

Answer 1

Let's draw the diagram.

Now,

• $\angle COD=120^\circ, \angle BAC=30^\circ$
• $\angle DAC=\frac{\angle COD}{2}=\frac{120^\circ}{2}=60^\circ$

$\angle DAB=\angle DAC+\angle BAC$

$\Rightarrow\angle DAB=60^\circ+30^\circ=90^\circ$

The $ABCD$ is a cyclic quadrilateral, the sum of the opposite angles will be $180^\circ$.

$\Rightarrow \angle DAB+\angle BCD=180^\circ$

$\Rightarrow 90^\circ+\angle BCD=180^\circ$

$\Rightarrow \angle BCD=180^\circ-90^\circ$

$\Rightarrow \boxed{\angle BCD=90^\circ}$

Correct Answer $:\text{D}$