EMAT 6700

Summary : Circles

by Doug Westmoreland


1. If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.

2. Tangents to a circle from a point are congruent.

3. In the same circle or in congruent circles:

a) Congruent minor arcs have congruent central angles. Congruent central angles have congruent arcs.

b) Congruent chords have congruent arcs. Congruent arcs have congruent chords.

c) Congruent chords are equally distant from the center. Chords equally distant from the center are congruent.

4. A diameter that is perpendicular to a chord bisects the chord and its arc.

5. If two inscribed angles intercept the same arc, then the angles are congruent.

6. If a quadrilateral is inscribed in a circle, then the opposite angles are supplementary.

7. An angle inscribed in a semicircle is a right angle.

8. Relationships expressed by formulas: