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1. The shortest distance from a point to a line is the perpendicular distance.
2. A tangent to a circle is perpendicular to the radius to the point of tangency.
3. If two lines from the same point are both tangent to a circle, then the line from the point to the center of the circle bisects the angle formed by the two tangents, and the point is equidistant from the two points of tangency.
4. A point is on the bisector of an angle if and only if the perpendicular distances from the point to both arms of the angle are the same.
5. The three angle bisectors of a triangle meet at the center of the inscribed circle.
6. The perpendicular bisectors of the three sides of a triangle all meet at the center of the circumscribed circle.
7. An inscribed angle in a circle is always half as big as the corresponding central angle.
8. The line from the midpoint of a chord to the center of the circle is perpendicular to the chord.