In a circle with centre `O ,` chords `A B\ a n d\ C D` intersect inside the circumference at `Edot` Prove that `/_A O C+\ /_B O D=2\ /_A E C`

Explanation

Consider AC of the circle with center at O.

Now, arc AC subtends `angleAOC` at the center and `angleABC` at the remaining part of the circle.

So, `angleAOC=2angleABC`____1

Similarly, arc BD subtends `angleBOD` at the center and `angleBCD` at the remaining part of the circle.

`therefore` `angleBOD=2angleBCD`___2

Adding 1 and 2

`angleAOC+angleBOD=2(angleABC+angleBCD)`

`angleAOC+angleBOD=2angleAEC`

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