Tangents. A tangent is a line in the same plane as a circle that intersects the circle in exactly one point, called the point of tangency. A common tangent.

Slides:

Advertisements

Similar presentations

Tangent/Radius Theorems

Advertisements

Definitions A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. Radius – the distance.

Chapter 12.1 Tangent Lines. Vocabulary Tangent to a circle = a line in the plane of the circle that intersects the circle in exactly one point.

10.5 Tangents & Secants.

Tangents Chapter 10 Section 5. Recall What is a Circle –set of all points in a plane that are equidistant from a given point called a center of the circle.

Section 9-2 Tangents.

Tangents Section Definition: Tangent  A tangent is a line in the plane of a circle that intersects the circle in exactly one point.

Tangents to Circles Pg 595. Circle the set of all points equidistant from a given point ▫Center Congruent Circles ▫have the same radius “Circle P” or.

Tangency. Lines of Circles EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord,

9 – 2 Tangent. Tangents and Circles Theorem 9 – 1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of.

Tangents Sec: 12.1 Sol: G.11a,b A line is ______________________ to a circle if it intersects the circle in exactly one point. This point.

Over Lesson 10–4 A.A B.B C.C D.D 5-Minute Check 1 60 Refer to the figure. Find m  1.

Circles – Tangent Lines A tangent line touches a circle at exactly one point. In this case, line t is tangent to circle A. t A.

Properties of Tangents of a Circle

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–4) Then/Now New Vocabulary Example 1:Identify Common Tangents Theorem Example 2:Identify.

6.1 Use Properties of Tangents

Section 10.1 cont. Tangents. A tangent to a circle is This point of intersection is called the a line, in the plane of the circle, that intersects the.

Friday, January 22 Essential Questions

Geometry Honors Section 9.2 Tangents to Circles. A line in the plane of a circle may or may not intersect the circle. There are 3 possibilities.

9 th Grade Geometry Lesson 10-5: Tangents. Main Idea Use properties of tangents! Solve problems involving circumscribed polygons New Vocabulary Tangent.

Warm-Up Exercises 1. What measure is needed to find the circumference or area of a circle? 2. Find the radius of a circle with diameter 8 centimeters.

Lesson 9.3A R.4.G.6 Solve problems using inscribed and circumscribed figures.

5-Minute Check on Lesson 10-4 Transparency 10-5 Click the mouse button or press the Space Bar to display the answers. Refer to the figure and find each.

Properties of Tangents. EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord, diameter,

 The tangent theorem states that if two segments are tangent to a circle and intersect one another, the length from where the segments touch the circle.

11-1 Tangent Lines Learning Target: I can solve and model problems using tangent lines. Goal 2.03.

CIRCLES: TANGENTS. TWO CIRCLES CAN INTERSECT… in two points one point or no points.

Tangent Applications in Circles More Problems Using Pythagorean Theorem.

Tangents. Definition - Tangents Ray BC is tangent to circle A, because the line containing BC intersects the circle in exactly one point. This point is.

EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent.

Circle GEOMETRY Radius (or Radii for plural) The segment joining the center of a circle to a point on the circle. Example: OA.

Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc.,

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–4) CCSS Then/Now New Vocabulary Example 1:Identify Common Tangents Theorem Example.

10-5 Tangents You used the Pythagorean Theorem to find side lengths of right triangles. Use properties of tangents. Solve problems involving circumscribed.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–4) NGSSS Then/Now New Vocabulary Example 1:Identify Common Tangents Theorem Example.

9-5 Tangents Objectives: To recognize tangents and use properties of tangents.

Tangents May 29, Properties of Tangents Theorem: If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point.

11-1 Tangent Lines Objective: To use the relationship between two tangents from one point.

 One way we can prove that a line is tangent to a circle is to use the converse of the Pythagorean Theorem.

Splash Screen. Then/Now You used the Pythagorean Theorem to find side lengths of right triangles. Use properties of tangents. Solve problems involving.

1. What measure is needed to find the circumference

Properties of Tangents

Section 10.5 Notes: Tangents Learning Targets Students will be able to use properties of tangents. Students will be able to solve problems involving.

Use Properties of Tangents

Introduction Circles and tangent lines can be useful in many real-world applications and fields of study, such as construction, landscaping, and engineering.

EXAMPLE 4 Verify a tangent to a circle

Warm-Up #33 3. Find x. 1. What is the perimeter of a regular hexagon if one of the side is 10 inches. 2. Find x X = 36 degrees Perimeter = 60 units X =

10-5: Tangents.

Tangents Tangent - A line in the plane of a circle that intersects the circle in exactly one point. Point of Tangency – The point of intersection between.

If m RU = 30, m RS = 88, m ST = 114, find: m∠S m∠R Problem of the Day.

EXAMPLE 1 Identify special segments and lines

Introduction Circles and tangent lines can be useful in many real-world applications and fields of study, such as construction, landscaping, and engineering.

LESSON 10–5 Tangents.

9-2 Tangents Theorem : If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.

Chapter 9 Section-2 Tangents.

Geometry Section 10.1.

EXAMPLE 1 Identify special segments and lines

Chapter 9 Section-2 Tangents.

Geometry Lesson: 10 – 5 Tangents Objective:

LESSON 10–5 Tangents.

Polygons: Inscribed and Circumscribed

To recognize tangents and use the properties of tangents

Tangents to Circles.

Five-Minute Check (over Lesson 9–4) Mathematical Practices Then/Now

Section 10-1 Tangents to Circles.

Tangents Solve problems involving circumscribed polygons.

Presentation transcript:

Tangents

A tangent is a line in the same plane as a circle that intersects the circle in exactly one point, called the point of tangency. A common tangent is a line, ray, or segment that is tangent to two circles in the same plane. In each figure below, in l is a common tangent of circles F and G.

Example 1: a) Using the figure below, draw the common tangents. If no common tangent exists, state no common tangent. These circles have no common tangents. Any tangent of the inner circle will intercept the outer circle in two points.

Example 1: b) Using the figure below, draw the common tangents. If no common tangent exists, state no common tangent. These circles have 2 common tangents.

Example 2: Test to see if ΔKLM is a right triangle. ? = 29 2 Pythagorean Theorem 841 =841 Simplify.

Example 2: Test to see if ΔXYZ is a right triangle. ? = 21 2 Pythagorean Theorem 452 ≠441Simplify.

Example 3: EW 2 + DW 2 =DE 2 Pythagorean Theorem x 2 =(x + 16) 2 EW = 24, DW = x, and DE = x x 2 =x x + 256Multiply. 320 =32xSimplify. 10 =xDivide each side by 32.

Example 3: JK 2 + KI 2 =IJ 2 Pythagorean Theorem x =(x + 8) 2 JK = x, KI = 16, and JI = x + 8 x =x x + 64Multiply. 192 =16xSimplify. 12 =xDivide each side by 16.

Example 4: AC =BCTangents from the same exterior point are congruent. 3x + 2 =4x – 3Substitution 2 =x – 3Subtract 3x from each side. 5 =xAdd 3 to each side.

Example 4: MN =MPTangents from the same exterior point are congruent. 5x + 4 =8x – 17Substitution 4 =3x – 17Subtract 3x from each side. 21 = 3xAdd 17 to each side. 7 =xDivide each side by 7.

Circumscribed Polygons A polygon is circumscribed about a circle if every side of the polygon is tangent to the circle.

Example 5: a) The round cookies are marketed in a triangular package to pique the consumer’s interest. If ∆QRS is circumscribed about T, find the perimeter of ∆QRS.

Find the perimeter of ΔQRS.

Example 5: b) A bouncy ball is marketed in a triangular package to pique the consumer’s interest. If ∆ABC is circumscribed about G, find the perimeter of ∆ABC.

Find the perimeter of ΔQRS.