Question

Angle inscribed in a minor segment is

• A. acute
• B. obtuse
• C. right
• D. straight

Answer 1

Answer: (B)

obtuse

Let AB be any chord and O be the center of a circle

WKT angle subtended by an arc at the cener is twice the angle subtended by any part of the alternate segment of the circle.

$⟹\angle AOB=2\angle ACB$

$\angle AOB<{180}^{\circ }$

$2\angle <{180}^{\circ }$

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

Angle in major segment is acute

Now BA is major arc and angle AOB is angle formed by it in the alternate segment.

$2\angle AOB=m\left(arcBA\right)=360–m\left(arcAB\right)$

$2\angle ADB=360-\angle AOB$

$⟹2\angle ADB>360-280$

$⟹\angle ADB>{90}^{\circ }$

Angle in minor segment is obtuse