'O' is the center of the circle, AC is a tangent to a circle at point A. If ΔOAC is isosceles triangle then find the measure of ∠OCA

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'O' is the center of the circle, AC is a tangent to a circle at point A. If ΔOAC is isosceles triangle then find the measure of ∠OCA

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75 °

50 °

45 °

40 °

answer is C.

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Detailed Solution

Let us first draw diagram for better understanding:

Let O be the center of the circle and let AC be the tangent to the circle. Join OA which is the radius of the circle. Also the joint OC which forms the triangle OAC.
As we know, the radius of a circle is perpendicular to the tangent of the circle. Therefore