AC-tangent, AB-chord of a circle centered at o, BAC-75 degrees What is AOB?

By the property of a tangent drawn to a circle, the radius drawn to the tangent from the center of the circle is perpendicular to the tangent. Then the angle CAO = 90.

Then the angle BAO = CAB – BAC = 90 – 75 = 15.

Triangle AOB is isosceles, since OA and OB are circular radii, then the angle ABO = BAO = 15.

Then the angle AOB = 180 – ABO – BAO = 180 – 15 – 15 = 150.

Answer: Angle AOB is 150.




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