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Constrained Tangent?

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Is there any way to create a line tangent to a circle where the line is constrained by an angle such as 90?, 45? or an angle entered into the data bar? For example, when I start a line tangent to a circle and hold the shift key down to constrain the line, the line is tangent to the circle, but the angle of the line is not constrained. Even if I enter an angle in the data bar, the angle is ignored and the line placed is at an imprecise angle.

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