1. Tangent is Perpendicular to Radius Tangent to the circle is perpendicular to the radius at the point of tangency.
Proof:
Proof by contradiction Let there be some other point, B, on the tangent line so that OB is at right angles to the tangent. OB will be longer than the radius as the tangent intersects the circle at only one point. Perpendicular distance from a point to the line is the shortest distance. Therefore, B should coincide with A.
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