Question

In the figure, if OA = OB = OC, then prove that
x + y = 2(z + t)​

Answer 1

Answer:

You can see the example of this chapter

Answer 2

Proved below.

Step-by-step explanation:

Given:

OA = OB = OC

To prove:

x + y = 2(z + t)

Proof:

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 arc AB, that subtends ∠AOB at centre and ∠ACB at any point on circle, then

∠AOB = 2∠ACB

⇒ x = 2t                    [1]

Consider the arc BC, that subtends ∠BOC at centre and ∠BAC at any point on circle, then

∠BOC = 2∠BAC

⇒y = 2z                   [2]

Adding Eq (1) and (2), we get    

x + y = 2z + 2t

⇒ x + y = 2(z+t)

Hence proved.