Question

In an art class, suneha sketched a design using geometrical shapes with the help of colours in the following way:

If in the figure, circles in black and blue are the circumcircle and incircle (of the equilateral $\Delta PQR)$ respectively, Then $\angle BAC$ is equal to

• A. ${120}^{\circ }$
• B. ${60}^{\circ }$
• C. ${30}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is B

${60}^{\circ }$

Given two concentric circles with radius O. Now, PQ, QR and PR are sides of equilateral $\Delta PQR$.
We have,
$\Rightarrow \angle QPR={60}^{\circ }\therefore \angle QOR={120}^{\circ }$
Also, in smaller circle.
$\angle BAC=\frac{1}{2}\angle BOC=\frac{1}{2}\angle QOR\therefore \angle BAC={60}^{\circ }$
[angle subtended by an arc at the centre is twice the angle subtended by the same arc in the remaining part]