Question

in the given figure, O is the centre of the circle. Prove that angle a+ angle b = angle c

Answer 1

in ∆ ACF side CF is produced to B
angle b = angle ACF+ angle FAC ........ (1)
In ∆ AED side ED produced to B
angle DAE +angle a = angle ADB ...........(2)
from 1 and 2, we have
angle DAE + Angle a+ angle b= angle FAC + angle ACF + angle ADB
angle a+ angle b= angle ACF ( angle ACF = angle ADB )
= angle c ( angle AOB = 2angle ACF )
hence ,
angle a+ angle b=angle c