9.6 Secants, Tangents and Angle Measures

Slides:

Advertisements

Similar presentations

Other Angle Relationships in Circles Section 10.4

Advertisements

Classifying Angles with Circles

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.

Other Angle Relationships

Bellwork  One-half of the measure of an angle plus its supplement is equal to the measure of the angle. Find the measure of the angle  Solve for x 2x.

Apply Other Angle Relationships in Circles

Warm-Up: 1)simplify: (x – 1)² 2)Factor: 10r² – 35r 3) Factor: t ² + 12t ) Solve: 2x ² – 3x + 1 = x ² + 2x – 3 5) Find the radius of a circle with.

Geometry Section 10.4 Angles Formed by Secants and Tangents

Secants, Tangents, and Angle Measures

12.4 Other Angle Relationships in Circles

Find an angle measure inside a circle

B D O A C Aim: What is a circle? Homework: Workbook page 370

Inscribed Angles Find measures of inscribed angles Find measures of angles of inscribed polygons. Three congruent central angles are pictured. What is.

Section 10.3 Inscribed Angles Geometry April 10, 2004.

10.4 Use Inscribed Angles and Polygons. Inscribed Angles = ½ the Measure of the Intercepted Arc 90 ̊ 45 ̊

5-Minute Check Other Angle Relationships in Circles February 26, 2013.

Geometry – Inscribed and Other Angles

SECANTS Secant - A line that intersects the circle at two points.

Angles, Circles, and parts of Circles. secant: a line, ray, or segment that contains a chord chord: segment has endpoints on circle tangent: a line, ray,

Secants, Tangents and Angle Measures. Definition - Secant.

6.5 Other Angle Relationships in Circles

6.5Apply Other Angle Relationships Theorem 6.13 If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one.

10.4 Other Angle Relationships in Circles

CIRCLES Everything you wanted to know and then some!!

Inscribed Angles December 3, What is an inscribed angle? An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords.

Section 10.5 Angles in Circles.

6.5 Other Angle Relationships in Circles. Theorem 6.13 If a tangent and a chord intersect at a point on the circle, then the measure of each angle formed.

Geometry Warm-Up4/5/11 1)Find x.2) Determine whether QR is a tangent.

Check.4.40 Find angle measures, intercepted arc measures, and segment lengths formed by radii, chords, secants, and tangents intersecting inside and outside.

10.1 Tangents to Circles. Some definitions you need Circle – set of all points in a plane that are equidistant from a given point called a center of the.

Section 10.4 Other Angle Relationships in Circles.

10.5 Apply Other Angle Relationships in Circles

Other Angle Relationships in Circles

Apply Other Angle Relationships in Circles

10.4 Other Angle Relationships in Circles

Other Angle Relationships in Circles

Module 19: Lesson 5 Angle Relationships in Circles

10.6 Secants, Tangents, and Angle Measures

Lesson 10.6 – Secants, Tangents, and Angle Measure

Find an angle measure inside a circle

1. 2x = Solve for x. ANSWER x = ( 360 – 120) = ANSWER 120.

Section 10.5 Angles in Circles.

Lesson: Angle Measures and Segment Lengths in Circles

11.4 Angle Measures and Segment Lengths

1. 2x = Solve for x. ANSWER x = ( 360 – 120) 1 2 ANSWER 120

Other Angle Relationships in Circles

Do Now One-half of the measure of an angle plus the angle’s supplement is equal to the measure of the angle. Find the measure of the angle.

Angle Measures and Segment Lengths in Circles

Chapter 10.5 Notes: Apply Other Angle Relationships in Circles

Geometry – Inscribed and Other Angles

9-6 Other Angles.

Circles – Modules 15.5 Materials: Notes Textbook.

Section 6.2 More Angle Measures in a Circle

Angles Related to a Circle

Apply Other Angle Relationships

Secants, Tangents, and Angle Measure

Other Angle Relationships in Circles

10.4 Other Angle Relationships in Circles

Warm-up #2 ( Find x and m AD B 72o A C 9xo D.

Unit 9 – Circles Acc. Alg/Geo A

Section 10.4 – Other Angle Relationships in Circles

EXAMPLE 1 Find angle and arc measures

Angles Related to a Circle

Notes 12.3/12.4 (Angles) Learning Targets:

Chapter 9 Section-6 Angles Other.

10.5 Other Angle Relationships in Circles

Do-Now Find the area of an equilateral triangle with side lengths of 26 ft. Reflect the point (3, –9) in the line y = x and state the coordinates of the.

Secants, Tangents, and Angle Measures

More Angle-Arc Theorems

Presentation transcript:

9.6 Secants, Tangents and Angle Measures Geometry

Objectives Use angles formed by tangents and chords to solve problems in geometry. Use angles formed by lines that intersect a circle to solve problems.

Using Tangents and Chords Measure of an angle inscribed in a circle is half the measure of its intercepted arc. m ADB = ½m AB

Theorem 9.11 If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc. m1= ½m AB m2= ½m ABC

Finding Angle and Arc Measures Line m is tangent to the circle. Find the measure of the red angle or arc. Solution: m1= ½ AB m1= ½ (150°) m1= 75° 150°

Finding Angle and Arc Measures Line m is tangent to the circle. Find the measure of the red angle or arc. Solution: m RSP = 2(130°) m RSP = 260° 130°

Finding an Angle Measure is tangent to the circle. Find m CBD Solution: m CBD = ½ m DAB 5x = ½(9x + 20) 10x = 9x +20 x = 20 mCBD = 5(20°) = 100° (9x + 20)° 5x° D

m1 = ½ ( m CD + m AB) m2 = ½ ( m BC+ m AD)

Finding the Measure of an Angle Formed by Two Chords 106° Find the value of x Solution: x° = ½ (m QR +m PS) x° = ½ (106° + 174°) x = 140 x° 174°

Using Theorem 9.13 Find the value of x 72° = ½ (200° - x°) m GHF = ½ (m EGD - m GF ) x° 72°

Using Theorem 9.13 Find the value of x = ½ (268 - 92) = ½ (176) = 88 Because MN and MLN make a whole circle, m MLN =360°-92°=268° x° 92° Find the value of x = ½ (268 - 92) = ½ (176) = 88 m GHF = ½ (m MLN - m MN)

Practice

Practice m1 = ½ ( 40 + 52) =46 m2 = ½ ( 134) = 67

Practice 100 = ½ ( 130 + x) 200 = 130+ x X = 70 50 = ½ ( (360 – x) -x)

CD = CQD = 120  E = ½ ( AD -BC) 25 = ½ (x -30) 50 = x – 30 X = 80 AB = 360-30 – 120 – 80 = AB = 130 QDC = (180- 120) / 2 = 30

360 = 140+ 2y + y +2y 360= 140 +5y 220 = 5y Y = 44 Y = 44 2 * 44 = 88 Y = 44 2 * 44 = 88 BCD = ½( AE – BD) BCD = ½( 140-44) BCD = 48

A = FB = 50 BCA = ½ * FB = 25 ABC = 180- 50 -25 = 105 GBC =180-105 =75 360 = 4x – 50 +x + x + 25+ x – 15 + 50 360=7x +10 350 = 7x X = 50 X = 50 CFD = ½*50 = 25 FHE = ½( 35 + 50) FHE = 42.5