Bidyut Guha Thakurta and Amitava Mitra Solutions for Exercise 1: EXERCISE 2

On the same arc the angle at the centre is equal to _____ times the angle at the circumference.

$O$ is the circumcentre of an equilateral triangle $ABC$ and$\angle AOB=x°$ . Then, the value of $x$ is _____.

The circumcentre of a triangle always lies inside the circle.

The circumcentre of the right-angled triangle is the midpoint of the hypotenuse.

The angle in a segment less than a semicircle is an acute angle.

A circle drawn on the hypotenuse of a right-angled triangle as diameter passes through the vertex opposite to the hypotenuse.

The circumference of a circle subtends an angle of measure $180°$ at the centre.

On the same arc if the angle at the centre is $140°$, then the angle at the circumference is $80°$.