Learning Target 17 Tangents Lesson 8-3: Tangents

Review: Circle Definition 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 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 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

THEOREM #1: If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. Example: Find the value of A B C D 4 3 A B C Lesson 8-3: Tangents

THEOREM #2: If two segments from the same exterior point are tangent to a circle, then they are congruent. B C A Example: Find the value of If AB = 1.8 cm, then AF = 1.8 cm AE = AF + FE AE = 1.8 + 7.0 = 8.8 cm If FE = 7.0 cm, then DE = 7.0 cm CE = CD + DE CE = 2.4 + 7.0 = 9.4 cm 2.4 cm 1.8 7.0 E A C F B D Lesson 8-3: Tangents

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

Learning Target #17 b Arcs Lesson 8-3: Tangents

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

Lesson 8-1: Circle Terminology Learning Target #17 c Chords Lesson 8-1: Circle Terminology

Lesson 8-4: Arcs and Chords Theorem 3: In a circle, two chords are congruent iff their corresponding minor arcs are congruent. E A B C D Example: Lesson 8-4: Arcs and Chords

Lesson 8-4: Arcs and Chords Theorem 4: In a circle, if a diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc. E D A C B Example: If AB = 5 cm, find AE. Lesson 8-4: Arcs and Chords

Lesson 8-4: Arcs and Chords Theorem 5: In a circle, two chords are congruent if and only if they are equidistant from the center. O A B C D F E Example: If AB = 5 cm, find CD. Since AB = CD, CD = 5 cm. Lesson 8-4: Arcs and Chords

Lesson 8-4: Arcs and Chords Try Some Sketches: Draw a circle with a chord that is 15 inches long and 8 inches from the center of the circle. Draw a radius so that it forms a right triangle. How could you find the length of the radius? Solution: ∆ODB is a right triangle and 8cm 15cm O A B D x Lesson 8-4: Arcs and Chords