Question

Angle in a minor segment is.

• A. An acuteangle
• B. An obtuse angle
• C. A right angle
• D. A reflexive angle

Answer 1

Answer: (B)

An obtuse angle

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

To prove: angle ADB is obtuse.

Construction: Join OA and OB

BA is the major arc and angle ADB is the angle formed by it in the alternate segment

$\therefore 2\angle ADB=m\left(arcBA\right)$

$=2\angle ADB={360}^{\circ }-m\left(arcAB\right)$

$=2\angle ADB={360}^{\circ }-\angle AOB\left(since\right(arcAB)=angleAOB)$

$=2\angle ADB>{360}^{\circ }-{180}^{\circ }(\because \angle AOB<{180}^{\circ })$

$=\angle ADB>{90}^{\circ }$

$=\angle ADB$ is obtuse.