#1**+2 **

I find a picture helps, here

Let BAC = 47°

Note that angles ABO and ACO each = 90°

So....the quadrilatral formed by ABOC has interior angles that will sum to 360°

And we know three of the angles and we are trying to find angle BOC

So

47 + 90 + 90 + BOC = 360 .......simplify

227 + BOC = 360 subtract 227 from both sides

BOC = 133

And since this is a central angle, it has the same measure as the arc we are interested in, namely, minor arc BC......so....the measure of the arc intercepted by the tangents = 133°

CPhill
Apr 3, 2017