Question

In the given figure a .0 is the centre of the circle show that angle a OC is equal to angle a FC plus angle a EC

Answer 1

Given: In the given figure O is the centre of the circle.

To Prove:

Proof: In ΔBEC using exterior angle theorem.

Exterior angle theorem property: Sum of two interior angle of triangle is equal to opposite exterior angle. So, we get

   

Double the above equation both sides



Angle subtended on circle is half angle subtended at centre.  

 





 (∴ Angles subtended on same arc are equal)



In ΔFDC using exterior angle theorem.