GLOSSARY OF TERMS Arc – a part of a circle

Arc Length – the length of an arc which can be determined by using the proportion

r A = l

360 2 , where A is the degree measure of an arc, r is the radius of the circle, and l is the arc length

Central Angle – an angle formed by two rays whose vertex is the center of the circle

Common External Tangents – tangents which do not intersect the segment joining the centers of the two circles

Common Internal Tangents – tangents that intersect the segment joining the centers of the two circles

Common Tangent – a line that is tangent to two circles on the same plane Congruent Arcs – arcs of the same circle or of congruent circles with equal measures

Congruent Circles – circles with congruent radii

Degree Measure of a Major Arc – the measure of a major arc that is equal to 360 minus the measure of the minor arc with the same endpoints.

Degree Measure of a Minor Arc – the measure of the central angle which intercepts the arc

External Secant Segment – the part of a secant segment that is outside a circle

Inscribed Angle – an angle whose vertex is on a circle and whose sides contain chords of the circle

Intercepted Arc – an arc that lies in the interior of an inscribed angle and has endpoints on the angle

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Major Arc – an arc of a circle whose measure is greater than that of a semicircle

Minor Arc – an arc of a circle whose measure is less than that of a semicircle Point of Tangency – the point of intersection of the tangent line and the

circle

Secant – a line that intersects a circle at exactly two points. A secant contains a chord of a circle

Sector of a Circle – the region bounded by an arc of the circle and the two radii to the endpoints of the arc

Segment of a Circle – the region bounded by an arc and a segment joining its endpoints

Semicircle – an arc measuring one-half the circumference of a circle

Tangent to a Circle – a line coplanar with the circle and intersects it at one and only one point

List of Theorems And Postulates On Circles Postulates:

1. Arc Addition Postulate. The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

2. At a given point on a circle, one and only one line can be drawn that is tangent to the circle.

Theorems:

1. In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding central angles are congruent.

2. In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

3. In a circle, a diameter bisects a chord and an arc with the same endpoints if and only if it is perpendicular to the chord.

4. If an angle is inscribed in a circle, then the measure of the angle equals one-half the measure of its intercepted arc (or the measure of the intercepted arc is twice the measure of the inscribed angle).

5. If two inscribed angles of a circle (or congruent circles) intercept congruent arcs or the same arc, then the angles are congruent.

6. If an inscribed angle of a circle intercepts a semicircle, then the angle is a right angle.

7. If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

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

9. If a line is perpendicular to a radius of a circle at its endpoint that is on the circle, then the line is tangent to the circle.

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10. If two segments from the same exterior point are tangent to a circle, then the two segments are congruent.

11. If two secants intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

12. If a secant and a tangent intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

13. If two tangents intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

14. If two secants intersect in the interior of a circle, then the measure of an angle formed is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

15. If a secant and a tangent intersect at the point of tangency, then the measure of each angle formed is one-half the measure of its intercepted arc.

16. If two chords of a circle intersect, then the product of the measures of the segments of one chord is equal to the product of the measures of the segments of the other chord.

17. If two secant segments are drawn to a circle from an exterior point, then the product of the lengths of one secant segment and its external secant segment is equal to the product of the lengths of the other secant segment and its external secant segment.

18. If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the length of the tangent segment is equal to the product of the lengths of the secant segment and its external secant segment.

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