Is a shape formed of two tangents and radii symmetrical?

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Is the kite formed by the two tangents and radii in this image symmetrical? Is there a law or reason why? I am assuming that the two tangents are of equal length, but I can't see why. Are any two tangents that meet equal in length?
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Hint: any tangent line is perpendicular to the radius joining the center to the point of tangency. From that it follows $AD=AB$, because triangles $AOD$ and $AOB$ are equal.