Because OA=OC=OB

So ∠ ACO = ∠ BAC = 30.

And AB is the diameter of a circle, so ∠ ACB = 90.

ME is perpendicular to AB, so ∠ EMB = 90.

So ECF = BAC = 30.

∠ECF=∠E here we go again

So ECF = 30.

Then ∠ fcn = 90-30 = 60

So ∠ FCO = ∠ FCN+∠ ACO = 90.

That is, CF is perpendicular to OC, so CF is the tangent of circle O.

2. If the radius of circle O is 1, then AB=2.

AC=√3 BC= 1 so CE=√3.

MO = BE * sinE-OB = 1/2( 1+√3)- 1 = 1/2(√3- 1)