# What is the measure of $\angle AOC$?

A circle with center O is inscribed in a quadrilateral ABCD. AB// CD, $\angle BCD$ = 60 and $\angle ADC$ = 40. What is the measure of $\angle$ AOC ?

My Try: If E, F, G, H are the points on AB, BC, CD, DA where those lines touch the circle, then OE is perpendicular to AB, OF perp to BC etc.

Also, when two tangents meet at a point outside the circle, the lengths of the two tangents are equal: AE = AH, BE=BF etc.

So if I draw these in, you get 4 pairs of congruent right-angled triangles OAE, OAH etc. Since they're congruent, the angles ADC and BCD are bisected by OD, OC.

I have no idea how to proceed from here. Could someone do the remaining angles part? Please