Question

$BC$ is a chord of a circle with centre $O$.A is a point on major are $BC$.Find the total measure of $\angle BACand\angle OBC.$

• A. $90°$
• B. $100°$
• C. $120°$
• D. $150°$

Answer 1

The correct option is A

$90°$

Step 1: Given data-

As per the data given in the question figure,

Considering the $∆OBC$

In $∆OBC,OB=OC(=radius)$

$\Rightarrow \angle OBC=\angle OCB=y$

Step 2: Applying the angle sum property

Now, $z+y+y=180°----\left(i\right)$

$\Rightarrow z=180°-2y$

Also,$\angle BOC=2\angle BAC$

$\Rightarrow z=2x-----\left(ii\right)$

Step 3: Calculation

From (1) and (2),

$$\begin{gathered} \Rightarrow 2x+2y=180° \\ \Rightarrow x+y=90° \end{gathered}$$

$\therefore \angle BAC+\angle OBC=90°$

Hence, option (A) is the correct choice.