Circles

10.1-10.2

Basic Things about Circles A circle is defined by it’s center and all points equally distant from that center. You name a circle according to it’s center point. The radius of a circle is the segment from it’s center to any point on the circle. A chord is a segment whose endpoints lie on the circle.

Basic Things about Circles The diameter of circle is twice the radius. The diameter is the longest chord and passes through the center.

Basic Things about Circles A tangent is a line that touches the circle at only one point. A secant is a lines that passes through the circle touching it in exactly two points. Line AB is a secant line. Line CD is a tangent line.

Central Angles A central angle is an angle whose vertex is at the center of the circle. is a central angle

Minor arcs The measure of a minor arc is equal to the measure of its central angle. A minor arc measures less than 180° When naming a minor arc, we use two letters and the arc symbol. For example minor arc AB, we use the notation

Major Arcs A major arc measures more than 180 It’s measure is 360 – the minor arc When naming a it you must use 3 points on the arc to show it is major along with the arc symbol. For example, major arc ADB is noted

Semicircle A semicircle is half the circle. Its endpoints are the endpoints of a diameter. You must use three letters to name a semicircle.

Notation When talking about the degree measure of an arc, we use the notation

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

Find the measure of each indicated arc below for circle P shown

Congruent circles have the same radius. Congruent arcs have the same measure and lie in the same circle or congruent circles.

Tell whether the red arcs are congruent.

Tangent Line to a Circle Theorem The tangent of a circle is perpendicular to the radius at the point of tangency.

Using Tangent Lines

External Tangent Congruence Theorem Tangent segments from a common external point are congruent.

practice P.538: 5-10, 19-25(odds), 29, 31 P.546: 3-15(odds), 19, 21