Lesson 8-1: Circle Terminology

Lesson 8-1: Circle Terminology Circle Definition Circle : The set of points coplanar points equidistant from a given point. The given point is called the CENTER of the circle. The distance from the center to the circle is called the RADIUS. Center Radius Lesson 8-1: Circle Terminology

Lesson 8-1: Circle Terminology Definitions Chord : The segment whose endpoints lie on the circle. Diameter : A chord that contains the center of the circle. Tangent : A line in the plane of the circle that intersects the circle in exactly one point. Tangent Point of Tangency : Chord The point where the tangent line intersects the circle. Diameter Secant : A line that contains a chord. Secant Lesson 8-1: Circle Terminology

Lesson 8-1: Circle Terminology Example: In the following figure identify the chords, radii, and diameters. Chords: O D A B F C E Radii: Diameter: Lesson 8-1: Circle Terminology

Lesson 8-1: Circle Terminology Definitions Congruent Circles : Circles that have congruent radii. 2 2 Concentric circles : Circles that lie in the same plane and have the same center. Lesson 8-1: Circle Terminology

Lesson 8-1: Circle Terminology Polygons Inscribed Polygon: A polygon inside the circle whose vertices lie on the circle. Circumscribed Polygon : A polygon whose sides are tangent to a circle. Lesson 8-1: Circle Terminology

Lesson 8-1: Circle Terminology ARCS Arcs : The part or portion on the circle from some point B to C is called an arc. A B C Example: B Semicircle: An arc that is equal to 180°. O A Example: C Lesson 8-1: Circle Terminology

Lesson 8-1: Circle Terminology Minor Arc & Major Arc Minor Arc : A minor arc is an arc that is less than 180° A minor arc is named using its endpoints with an “arc” above. A Example: Major Arc: A major arc is an arc that is greater than 180°. B B O A major arc is named using its endpoints along with another point on the arc (in order). A Example: C Lesson 8-1: Circle Terminology

Lesson 8-1: Circle Terminology Example: ARCS Identify a minor arc, a major arc, and a semicircle, given that is a diameter. Minor Arc: A C D E F Major Arc: Semicircle: Lesson 8-1: Circle Terminology

Formulas Lesson 8-2 Circumference Arc Length Area Sector Lesson 8-2: Formulas

Central Angle A central angle is an angle whose vertex is at the center of the circle. The arc measure is written as The measure of a minor arc is the measure of its central angle. The measure of a major arc is 360 minus the measure of its central angle. Lesson 8-2: Formulas

CIRCUMFERENCE: Circumference is the distance around the circle. Formula: Or where Example: Find the circumference of the following circle. 3 cm cm Lesson 8-2: Formulas

Arc Length Arc length is the distance around an arc. Formula: The circumference multiplied by the ratio of the center angle and 360°. Example: Arc Length 2 cm 72 ° B C A Lesson 8-2: Formulas

Area of a Circle Area of a circle is the number of unit squares that can fit into a circle. Formula: Example: Find the area of the following circle. 3 cm Lesson 8-2: Formulas

Area of a Sector Area of a sector is the area of a section of the circle. Formula: The area multiplied by the ratio of the center angle and 360° Example: Sector 65° Lesson 8-2: Formulas