Question

4. Prove that the angles in a same segment of a circle are equal.​

Answer 1

Answer , Explanation:

Given - A circle with centre at O .

To Prove - angle poq = 2 angle paq .

Proof - angle poq = angle paq -------- 1.

Similarly

POQ =2 PBQ

From 1

2 PBQ = 2 PAQ

Angle PBQ = Angle PAQ .

Hence Proved :)

Answer 2

Answer:

∠APB and ∠AQB are in the same segment of a circle with centre O.

To Prove: ∠APB = ∠AQB

Construction: Join AO and BO.

Let arc AMB subtend angle x at the centre O.

proof:1.angle X =2 angleAPB angle at the centre point =2 x angle on the circumference

2.angleX =2 angle AQB angle at the centre point =2 x angle on the circumference

3. therefore,, angleAPB = angleAQB statements (1) (2)