prove that :

a) angle in the major segment of a circle is acute

b) angle in the minor segment of circle is obtuse

Question

prove that :
a) angle in the major segment of a circle is acute
b) angle in the minor segment of circle is obtuse

Lalit Mehra · Accepted Answer

Dear Student!

Given : ADB is the minor segment and ACB is the major segment of a circle C(0, r) âˆ ADB is the angle drawn in the minor segment and âˆ ACB is an angle drawn in the major segment To prove : âˆ ADB is obtuse and âˆ 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 âˆ´

is the minor arc and âˆ ACB is the angle subtended by it in alternate segment âˆ´ m

= 2 âˆ ACB $\Rightarrow ∠ AOB = 2 ∠ ACB \Rightarrow 2 ∠ ACB < 180 ° (∵ ∠ AOB is an angle of Δ ABC) \Rightarrow ∠ ACB < 90 °$ Thus, âˆ ACB is acute ACB is the major segment âˆ´

is the major arc and âˆ ADB is the angle subtended by it in alternate segment âˆ´ m

= 2 âˆ ADB $\Rightarrow 360 ° - ∠ AOB = 2 ∠ ADB \Rightarrow 2 ∠ ADB > 360° - 180 ° (∵ ∠ AOB < 180°) \Rightarrow 2 ∠ ADB > 180° \Rightarrow ∠ ADB > 90 ° T h u s, ∠ ADB is obtuse$ Cheers!

prove that : a) angle in the major segment of a circle is acute b) angle in the minor segment of circle is obtuse

prove that :

a) angle in the major segment of a circle is acute

b) angle in the minor segment of circle is obtuse