11.1 Tangent Lines Chapter 11 Circles.

Slides:



Advertisements
Similar presentations
Secants and Tangents Lesson 10.4 A B T. A B A secant is a line that intersects a circle at exactly two points. (Every secant contains a chord of the circle.)
Advertisements

10.1 Tangents to Circles.
Section 11-1 Tangent Lines SPI 32B: Identify chords of circles given a diagram SPI 33A: Solve problems involving the properties of arcs, tangents, chords.
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.
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.
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.
Circle. Circle Circle Tangent Theorem 11-1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of.
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.
Lesson 6.1 – Properties of Tangent Lines to a Circle
Welcome back. Warm up Use Pythagorean Theorem to find the missing side. Round to the nearest tenths. 8.2 yd 8.3 m 2.2 ft.
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.
Section 10 – 1 Use Properties of Tangents. Vocabulary Circle – A set of all points that are equidistant from a given point called the center of the circle.
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.
Ch 11 mini Unit. LearningTarget 11-1 Tangents I can use tangents to a circle to find missing values in figures.
12-1 Tangent Lines. Definitions A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point called the.
6.1 Use Properties of Tangents
Chapter 11 Circles.
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.
Section 9.1 Basic terms of Circles Circles. What is a circle? Circle: set of points equidistant from the center Circle: set of points equidistant from.
Chapter 6 Circles Exploring Circles 3 Circle Vocabulary Circle – set of all points equidistant from a point Chord – segment whose endpoints are.
 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.
Lesson 7.3. If the diameter of a circle is 15 units in length, how long is the circle's radius?(answer in a decimal)
Circle GEOMETRY Radius (or Radii for plural) The segment joining the center of a circle to a point on the circle. Example: OA.
Chapter 12 Circles Vocab. Circle – the set of all points in a plane a given distance away from a center point. A A circle is named by its center point.
Bell work 1 Find the measure of Arc ABC, if Arc AB = 3x, Arc BC = (x + 80º), and __ __ AB BC AB  BC AB = 3x º A B C BC = ( x + 80 º )
Tangents to Circles Geometry. Objectives/Assignment Identify segments and lines related to circles. Use properties of a tangent to a circle. Assignment:
GEOMETRY HELP BA is tangent to C at point A. Find the value of x x = 180 Substitute x = 180Simplify. x = 68 Solve. m A + m B + m C =
Lesson 8-1: Circle Terminology
10-5 Tangents You used the Pythagorean Theorem to find side lengths of right triangles. Use properties of tangents. Solve problems involving circumscribed.
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.
Tangents November 21, Properties of Tangents Theorem: If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the.
11-1 Tangent Lines Objective: To use the relationship between two tangents from one point.
Tangents November 18, Yesterday’s homework 1. What is the difference between a secant and a tangent to a circle? 2. Write the definition of a radius.
Circles and Pythagorean Theorem. Circle and Radius The radius of a circle is the distance from the center of the circle to any point on the circle, all.
Theorem 12-1: If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. Point of tangencyA B O P.
Spi.3.1 Use algebra and coordinate geometry to analyze and solve problems about geometric figures (including circles). Check.2.2 Approximate pi from a.
Warm Up 3-7 Write the standard form equation of the circle.
12.1 Parts of Circles and Tangent Lines Geometry.
10.7: Area of Circles and Sectors
Section 10.5 Notes: Tangents Learning Targets Students will be able to use properties of tangents. Students will be able to solve problems involving.
11.1; chord 22. tangent 23. diameter 24. radius
Tangent Lines A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point. The point where a circle and.
12-1 Tangent Lines.
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 =
Tangents to Circles A line that intersects with a circle at one point is called a tangent to the circle. Tangent line and circle have one point in common.
Day 2 of Circles 11-1 Tangent Lines.
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.
Circles and the Pythagorean Theorem
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.
Day 2 of Circles 11-1 Tangent Lines.
Tangents to Circles.
Chapter 9 Section-2 Tangents.
11-1 Tangent Lines Objective: To use the relationship between two tangents from one point.
NOTES 10.4 Secants and Tangents
Chapter 9 Section-2 Tangents.
Tangent Lines Skill 48.
12.1 Tangent Lines.
Tangents to Circles.
Section 10-1 Tangents to Circles.
Tangents Solve problems involving circumscribed polygons.
Presentation transcript:

11.1 Tangent Lines Chapter 11 Circles

Tangent to a circle: a line that touches the circle at one point Point of tangency: the point where the line and circle touch

Theorem 11-1: If a line is tangent to a circle, then it is perpendicular to the radius.

Lines ML and MN are tangents to Circle O. Find the value of x. What are the measures of <OLM and <ONM? 90° 117° O 117 + 90 + 90 + x = 360 N x = 63°

ED is tangent to Circle O. Find the value of x. 38° x = 52° O x° E D

A dirt bike chain fits tightly around two gears A dirt bike chain fits tightly around two gears. The chain and gears form a figure like the one below. Find the distance between the centers of the gears. C 26.5 in E 9.3 in B D 2.4 in A ABCE is a rectangle and AED is a right triangle. AE is 26.5 ED is 9.3 – 2.4 = 6.9 Use Pythagorean Theorem to solve for AD. 26.52 + 6.92 = c2 AD = 27.4 in

A chain fits tightly around two circular pulleys A chain fits tightly around two circular pulleys. Find the distance between the centers of the pulleys. 35in 14in 8in 352 + 62 = c2 c = 35.5in

If a line is perpendicular to the radius at its endpoint on the circle, then the line is tangent to the circle. Is ML tangent to Circle N at L? 72 + 242 = 252 ?? 49 + 576 = 625 ?? 25 M N 625 = 625 24 7 Yes, ML is tangent to circle N L

If all the vertices of a triangle are on a circle, the triangle is inscribed in the circle When a circle is inscribed in a triangle, the triangle is circumscribed about the circle.

The two segments tangent to a circle from a point outside the circle are ____________!

Ex. 3: Find the perimeter of the triangle! The two segments tangent to a circle from a point outside the circle are ____________! congruent Ex. 3: Find the perimeter of the triangle! 8 10 15 P = 10 + 10 + 15 + 15 + 8 + 8 P = 66

Circle O is inscribed in PQR. PQR has a perimeter of 88cm. Find QY. 15 + 15 + 17 + 17 + x + x = 88 x 64 + 2x = 88 x Y 2x = 24 X 17cm O x = 12 QY = 12 15cm P R Z 15cm 17cm

Homework: Pg 586-9: # 1 – 22