Question

Point o is the centre of the circle. Show that angle AOC=angle AFC+angle AEC

Answer 1

Angle Aoc=180degree

Angle Aec and Afc=90 degree

Angle Aoc=angle Afc+ Aec

Answer 2

In a circle,
< AEC + < AFC = 180°........( interior angle) ..(1)
In ∆ AOF & ∆ COF,
< AOF = < COF ..... ( common angle )
∆ AOF ~ ∆COF ... ...( AAA test ) ....(2)
From 1^st and 2^ nd
< AEC + < AFC = < AOF + < CFO
<AFC + <AFC = < AOC ...( < AOF + <CFO = <AOC )