prove that :
a) angle in the major segment of a circle is acute
b) angle in the minor segment of circle is obtuse
Dear Student!
Given : ADB is the minor segment and ACB is the major segment of a circle C(0, r).∠ADB is the angle drawn in the minor segment and ∠ACB is an angle drawn in the major segment.
To prove : ∠ADB is obtuse and ∠ACB is acute.
Proof : We know that, the angles subtended by an arc of a circle at its centre is twice the angle subtended by it at any point of the alternative segment of the circle.
ADB is the minor segment.
∴ is the minor arc and ∠ACB is the angle subtended by it in alternate segment.
∴ m = 2 ∠ACB
Thus, ∠ACB is acute.
ACB is the major segment.
∴ is the major arc and ∠ADB is the angle subtended by it in alternate segment.
∴ m = 2 ∠ADB
Cheers!