Question

In the following figure, O is centre of the circle and $\Delta ABC$ is equilateral. Which of the following is true?

• A. $\angle ACB={60}^{\circ }$
• B. $\angle AEB={120}^{\circ }$
• C. $\angle AEB={220}^{\circ }$
• D. $\angle ACB={130}^{\circ }$

Answer 1

Answer: (A), (B)

The correct options are
A

$\angle ACB={60}^{\circ }$

B

$\angle AEB={120}^{\circ }$

$\because \angle ACB$ and $\angle ADB$ are in the same segment.

$\therefore \angle ADB=\angle ACB={60}^{\circ }$

(Angle of an equilateral triangle)

$\because$ AEBD is a cyclic quadrilateral

$\therefore \angle AEB+\angle ADB={180}^{\circ }$

$\Rightarrow \angle AEB+{60}^{\circ }={180}^{\circ }$

$\therefore \angle AEB={180}^{\circ }-{60}^{\circ }={120}^{\circ }$