In the figure, O is the centre of the circle. Prove that XOZ-2(XZY LYX

1.	In the figure, O is the centre of the circle. Prove that XOZ-2(XZY LYXZ).
Answer» We know that,angle subtended by an arc at the centre is double the angle subtended by the same arc at any point on the circle. Consider the minor arc XY, that subtends ∠XOY at the centre and ∠XZY at the circle. Now, ∠XOY = 2 ∠XZY .......(1) Consider the minor arc YZ, that subtends ∠YOZ at the centre and ∠YXZ at the circle. Now, ∠YOZ = 2 ∠YXZ .......(2) adding (1) and (2), we get ∠XOY + ∠YOZ = 2∠XZY + 2 ∠YXZ ⇒∠XOZ = 2[∠XZY + ∠YXZ] like my answer if you find it useful!

In the figure, O is the centre of the circle. Prove that XOZ-2(XZY LYXZ).

Answer»

We know that,angle subtended by an arc at the centre is double the angle subtended by the same arc at any point on the circle.

Consider the minor arc XY, that subtends ∠XOY at the centre and ∠XZY at the circle.

Now, ∠XOY = 2 ∠XZY .......(1)

Consider the minor arc YZ, that subtends ∠YOZ at the centre and ∠YXZ at the circle.

Now, ∠YOZ = 2 ∠YXZ .......(2)

adding (1) and (2), we get ∠XOY + ∠YOZ = 2∠XZY + 2 ∠YXZ

⇒∠XOZ = 2[∠XZY + ∠YXZ]

like my answer if you find it useful!