Question

AD , AF , and DF are tangent to circle O through points C, B, and E, respectively. If mDAF = 66° and mFDA = 56°, what is mEOB?

Answer 1

Find <DFA first.
56 + 66 + X = 180
122 + x = 180
180 - 122 = 58
<DFA = 58

Tangent circle theorem : always perpendicular to the radius of a circle.
<OBF = 90 & <OEF = 90

All quadrilaterals have an interior sum of 360

90 + 90 + 58 + <EOB = 360
238 + <EOB = 360
360 - 238 = 122

<EOB = 122