Question

Angle in a major segment is.

• A. An acute angle
• B. An obtuse angle
• C. A right triangle
• D. A reflexive angle

Answer 1

The correct option is A An acute angle

Given : A minor segment AB of a circle and two points C and D in BA and AB. respectively.

To prove : angle ACB is acute

Construction : Join OA and OB

We know that angle subtended by an arc of a circle at its center is twice the angle subtended by it at any point of the alternate segment of circle. Since AB is minor arc and angle ACB is the angle formed by it in alternate segment.

$\therefore ,2\angle ACB=\angle AOB.$

$=2\angle ACB<{180}^{\circ }$ ( since $\angle AOB$ is an angle of triangle AOB)

$=\angle ACB<{90}^{\circ }$

$=\angle ACB$ is an acute angle.