Presentation is loading. Please wait.

Presentation is loading. Please wait.

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.

Published byGriselda Parks Modified over 9 years ago

Similar presentations

Presentation on theme: "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."— Presentation transcript:

1 Tangents

2 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.

3 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.

4 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.

5

6 Example 2: Test to see if ΔKLM is a right triangle. ? 20 2 + 21 2 = 29 2 Pythagorean Theorem 841 =841 Simplify.

7 Example 2: Test to see if ΔXYZ is a right triangle. ? 14 2 + 16 2 = 21 2 Pythagorean Theorem 452 ≠441Simplify.

8 Example 3: EW 2 + DW 2 =DE 2 Pythagorean Theorem 24 2 + x 2 =(x + 16) 2 EW = 24, DW = x, and DE = x + 16 576 + x 2 =x 2 + 32x + 256Multiply. 320 =32xSimplify. 10 =xDivide each side by 32.

9 Example 3: JK 2 + KI 2 =IJ 2 Pythagorean Theorem x 2 + 16 2 =(x + 8) 2 JK = x, KI = 16, and JI = x + 8 x 2 + 256 =x 2 + 16x + 64Multiply. 192 =16xSimplify. 12 =xDivide each side by 16.

10

11 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.

12 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.

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

14 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.

15 Find the perimeter of ΔQRS.

16 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.

17 Find the perimeter of ΔQRS.

Download ppt "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."

Similar presentations

Tangent/Radius Theorems

Tangent/Radius Theorems
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.

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.

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.

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.

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.

Section 9-2 Tangents.
Tangents Section 10.5. Definition: Tangent  A tangent is a line in the plane of a circle that intersects the circle in exactly one point.

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.

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,

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.

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.
1. 5. 4. 3. 2.. 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.

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.

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.

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

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 10.10 Example 2:Identify.

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

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.

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

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.

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.

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

Similar presentations

Ads by Google