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Question

In the given figure, O is the centre of the circle, prove that ∠x = ∠y + ∠z.


Solution

It is given that, O is the center of circle and A, B and C are points on circumference on triangle

  

We have to prove that x = ∠y + ∠z

∠4
and ∠3 are on same segment

So, ∠4 = ∠3           

               (Angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle)

…… (1)

               (Exterior angle is equal to the sum of two opposite interior angles)         …… (2)

4=z+1               (Exterior angle is equal to the sum of two opposite interior angles)  

                 …… (3)

Adding (2) and (3)

……(4)

From equation (1) and (4) we have 


Mathematics
RD Sharma (2019)
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