Presentation is loading. Please wait.

Presentation is loading. Please wait.

All you need to know about Circles! By: Ms. Erwin

Published byJordan Flowers Modified over 6 years ago

Similar presentations

Presentation on theme: "All you need to know about Circles! By: Ms. Erwin"β€” Presentation transcript:

1 All you need to know about Circles! By: Ms. Erwin
Circle Book Notes! All you need to know about Circles! By: Ms. Erwin

2 Day 1

3 Tangent Chord VOCAB Inscribed Angle Central Angle Secant

4 Major Arc Minor Arc A Minor Arc = 𝐴𝐡 Major Arc = 𝐴𝐢𝐡
A Minor Arc is named by two endpoints, and it measures between 0Β°<πœƒ<180Β° A Major Arc is named by Three points on the arc, and it Measures between πœƒ>180Β° Major Arc B E C Semicircle= 𝐡𝐷𝐢 We name a circle based on its β€œCenter” E is the Center We would call this circle, β€œCircle E” A circle measures exactly πœƒ=360Β° A Semicircle is named by Three points on the arc, and it Measures exactly πœƒ=180Β° D

5 Inscribed Quadrilateral Inscribed Quadrilateral:
F F 𝑬𝑿 𝟏: VOCAB: <𝐢𝐹𝐷 is an INSCRIBED ANGLE <π‘ͺ𝑭𝑫= 𝟏 𝟐 π’Ž 𝑩π‘ͺ Inscribed Quadrilateral A B C D B C E 𝑉𝑂𝐢𝐴𝐡: <𝐢𝐸𝐷 is a CENTRAL ANGLE <π‘ͺ𝑬𝑫=π’Ž 𝑫π‘ͺ Inscribed Quadrilateral: Opposite Angles are SUPPLEMENTARY! Central Angle 𝑬𝑿 𝟐: D

6 𝐄𝐗 𝟏: πŸ—πŸŽΒ°= π’Ž π‘ͺ𝑫 If <π‘ͺ𝑭𝑫=πŸ’πŸ“Β°, π’‡π’Šπ’π’… π’Ž π‘ͺ𝑫 <π‘ͺ𝑭𝑫= 𝟏 𝟐 π’Ž π‘ͺ𝑫
C D F If <π‘ͺ𝑭𝑫=πŸ’πŸ“Β°, π’‡π’Šπ’π’… π’Ž π‘ͺ𝑫 πŸ’πŸ“Β° <π‘ͺ𝑭𝑫= 𝟏 𝟐 π’Ž π‘ͺ𝑫 πŸ’πŸ“= 𝟏 𝟐 π’Ž π‘ͺ𝑫 πŸ—πŸŽΒ°= π’Ž π‘ͺ𝑫

7 EX 2: If Opposite angles are supplementary in an inscribed quadrilateral, find the following measure. <𝐷=71° Find the measure of <𝐡 A B C D <D+<B=180 71+<B=180 <B=109°

8 Day 2

9 Angle Relationships Angles formed by one Angles formed by CHORDS:
SECANT and one TANGENT: Angles formed by CHORDS: <𝐴𝐸𝐡 B A C D A B C D E <𝐴𝐸𝐡= 𝐴𝐡 + 𝐷𝐢 2 <𝐴𝐡𝐢= 𝐴𝐷𝐡 2 Angles formed by two SECANTS: Ex 3: Ex 4: Ex 5: Angle Relationships A C B F G <𝐴𝐡𝐢 <𝐴𝐡𝐢= 𝐴𝐢 βˆ’ 𝐹𝐺 2

10 Find the π‘š<𝐷𝐸𝐴 if π‘š 𝐷𝐴 =104Β°, π‘š 𝐷𝐢 =76Β°, π‘Žπ‘›π‘‘ π‘š 𝐴𝐡 =65Β°,
Ex 3: Ex 5: B A C D A B C D E 156Β° 65Β° π‘š 𝐡𝐢 =360Β°βˆ’ 104Β°+65Β°+76Β° 104Β° π‘š 𝐡𝐢 =115Β° <𝐷𝐸𝐴= 𝐷𝐴 + 𝐡𝐢 2 π‘š 𝐡𝐷𝐴 =360Β°βˆ’156Β° 76Β° <𝐷𝐸𝐴= 104Β°+115Β° 2 π‘š 𝐡𝐷𝐴 =204Β° <𝐷𝐸𝐴=109.5Β° <𝐢𝐡𝐴= 𝐡𝐷𝐴 2 <𝐢𝐡𝐴= 204Β° 2 Ex 4: Find the π‘š<𝐴𝐡𝐢 if π‘š 𝐴𝐹 =70Β°, π‘š 𝐺𝐢 =143Β°, π‘Žπ‘›π‘‘ π‘š 𝐴𝐢 =98Β°, 70Β° A C B F G π‘š 𝐹𝐺 =360Β°βˆ’ 70Β°+98Β°+143Β° <𝐢𝐡𝐴=102Β° π‘š 𝐡𝐢 =49Β° 98Β° <𝐴𝐡𝐢= 𝐴𝐢 βˆ’ 𝐹𝐺 2 143Β° <𝐴𝐡𝐢= 98Β°βˆ’49Β° 2 <𝐴𝐡𝐢=24.5Β°

11 Day 3-4

12 Segment Relationships
One Secant and one Tangent Intersect! Two Chords Intersect! A B C D E B A C D 𝐴𝐸 βˆ— 𝐸𝐢 = 𝐷𝐸 βˆ— 𝐸𝐡 𝐴𝐷 βˆ— 𝐡𝐷 = ( 𝐢𝐷 ) 2 Segment Relationships Two Secants Intersect! EX 6: EX 7: EX 8: A C B F G 𝐴𝐡 βˆ— 𝐹𝐡 = 𝐢𝐡 βˆ— 𝐺𝐡

13 EX 6: Find 𝐴𝐸 if 𝐸𝐡 =8, 𝐷𝐸 =6, and 𝐸𝐢 =12
C B F G A B C D E 𝐴𝐸 βˆ— 𝐸𝐢 = 𝐷𝐸 βˆ— 𝐸𝐡 𝐴𝐸 βˆ—12=6βˆ—8 𝐴𝐸 βˆ—12=48 EX 8: Find 𝐴𝐡 if 𝐢𝐡 =10, 𝐺𝐡 =5, and 𝐹𝐡 =4 𝐴𝐸 =4 𝐴𝐡 βˆ— 𝐹𝐡 = 𝐢𝐡 βˆ— 𝐺𝐡 EX 7: Find 𝐢𝐷 if 𝐴𝐡 =5, 𝐡𝐷 =4 𝐴𝐡 βˆ—4=10βˆ—5 𝐴𝐷 βˆ— 𝐡𝐷 = ( 𝐢𝐷 ) 2 B A C D 𝐴𝐡 βˆ—4=50 9βˆ—4= ( 𝐢𝐷 ) 2 𝐴𝐡 =12.5 36= ( 𝐢𝐷 ) 2 6= 𝐢𝐷

14 If two chords are congruent, then the arcs are congruent
B C If two chords are congruent, then the arcs are congruent 𝑖𝑓 𝐴𝐡 ≅𝐢𝐡 π‘‘β„Žπ‘’π‘› 𝐴𝐡 β‰… 𝐢𝐡 A C B D E If a radius or diameter is perpendicular to a chord, then the radius bisects the chord, and the arc. 𝑖𝑓 𝐴𝐷 𝑖𝑠 π‘π‘’π‘Ÿπ‘π‘’π‘›π‘–π‘π‘’π‘™π‘Žπ‘Ÿ π‘‘π‘œ 𝐡𝐢 π‘‘β„Žπ‘’π‘› 𝐡𝐷 β‰… 𝐢𝐷 and 𝐡𝐸 β‰… 𝐸𝐢 A C B D E F G H I Two chords are congruent, if and only if they are equidistant from the center. 𝐺𝐻 β‰… 𝐡𝐢 𝑖𝑓 π‘Žπ‘›π‘‘ π‘œπ‘›π‘™π‘¦ 𝑖𝑓 𝐴𝐸 β‰… 𝐴𝐸

15 A line is tangent to a circle if and only if
it is perpendicular to a radius drawn at the point of tangency 𝐢𝐴 𝑖𝑠 π‘‘π‘Žπ‘›π‘”π‘’π‘›π‘‘ π‘‘π‘œ π‘π‘–π‘Ÿπ‘π‘™π‘’ 𝑇. 𝐴 𝑖𝑠 π‘‘β„Žπ‘’ π‘π‘œπ‘–π‘›π‘‘ π‘œπ‘“ π‘‘π‘Žπ‘›π‘”π‘’π‘›π‘π‘¦ A C T Z X Y If two segments from the same exterior point are tangent to a circle, then they are congruent π‘Œπ‘ π‘Žπ‘›π‘‘ π‘Œπ‘‹ π‘Žπ‘Ÿπ‘’ π‘‘π‘Žπ‘›π‘”π‘’π‘›π‘‘ π‘‘π‘œ π‘‘β„Žπ‘’ π‘π‘–π‘Ÿπ‘π‘™π‘’. π‘‡β„Žπ‘’π‘ . π‘Œπ‘ β‰… π‘Œπ‘‹

16 Day 5

17 Arc Length Sector Area A piece of the circumference of a circle
A slice of the circle bounded by 2 radii and an arc π΄π‘Ÿπ‘ πΏπ‘’π‘›π‘”π‘‘β„Ž= π‘₯Β° 360Β° βˆ—2πœ‹π‘Ÿ π‘†π‘’π‘π‘‘π‘œπ‘Ÿ π΄π‘Ÿπ‘’π‘Ž= π‘₯Β° 360Β° βˆ—πœ‹ π‘Ÿ 2 Ex 9: Find the length of arc 𝐸𝐹 in circle S if ES=6 Ex 10: Find the area of the blue sector in Cricle M if AM=5 and 𝐴𝑅 =150Β° E F S A R M

18 Ex 9: 𝐹𝑖𝑛𝑑 π‘‘β„Žπ‘’ π‘™π‘’π‘›π‘”π‘‘β„Ž π‘œπ‘“ π‘Žπ‘Ÿπ‘ 𝐸𝐹
𝑖𝑛 π‘π‘–π‘Ÿπ‘π‘™π‘’ 𝑆 𝑖𝑓 𝐸𝑆=6𝑖𝑛, π‘Žπ‘›π‘‘ π‘š<𝐸𝑆𝐹=60Β° π΄π‘Ÿπ‘ πΏπ‘’π‘›π‘”π‘‘β„Ž= π‘₯Β° 360Β° βˆ—2πœ‹π‘Ÿ E F S 𝐸𝐹 = 60Β° 360Β° βˆ—2πœ‹βˆ—6 𝐸𝐹 =6.3 𝑖𝑛 Ex 10: Find the area of the blue sector in Cricle M if AM=5cm and 𝐴𝑅 =150Β° π‘†π‘’π‘π‘‘π‘œπ‘Ÿ π΄π‘Ÿπ‘’π‘Ž= π‘₯Β° 360Β° βˆ—πœ‹ π‘Ÿ 2 A R M π‘†π‘’π‘π‘‘π‘œπ‘Ÿ π΄π‘Ÿπ‘’π‘Ž= 150Β° 360Β° βˆ—πœ‹ 5 2 π‘†π‘’π‘π‘‘π‘œπ‘Ÿ π΄π‘Ÿπ‘’π‘Ž=32.7 π‘π‘š 2

19 Day 6

20 Radian Measure We indicate radian measure using the symbol for a central angle 𝜽 𝑻𝒉𝒆 π’ˆπ’“π’†π’†π’Œ 𝒍𝒆𝒕𝒕𝒆𝒓 𝑻𝒉𝒆𝒕𝒂 Radian measure is the ratio of the arc length, l, to the radius of the circle 𝜽= 𝒍 𝒓 πŸ‘πŸ”πŸŽΒ°=πŸπ… π’“π’‚π’…π’Šπ’‚π’π’”

21 So if πŸ‘πŸ”πŸŽΒ°=πŸπ… π’“π’‚π’…π’Šπ’‚π’π’”, then what would πŸπŸ–πŸŽΒ°π’ƒπ’† π’Šπ’ π’“π’‚π’…π’Šπ’‚π’π’”?
πŸπŸ–πŸŽΒ°=𝝅 π’“π’‚π’…π’Šπ’‚π’π’” Lets see if we can come up with more radian measures 𝝅 𝟐 𝝅 𝟐 90Β°= ___________π‘Ÿπ‘Žπ‘‘π‘–π‘Žπ‘›π‘  𝝅 πŸπ… πŸ‘π… 𝟐 270Β°= ___________π‘Ÿπ‘Žπ‘‘π‘–π‘Žπ‘›π‘  πŸ‘π… 𝟐

22 Ex 1:

23 You Try!

24 You Try!

25 Equation of a Circle β€œCenter-Radius Form”
Any circle can be expressed in the standard form (π‘₯βˆ’β„Ž) 2 + (π‘¦βˆ’π‘˜) 2 = 𝒓 2 Where the center of the circle is at the point β„Ž,π‘˜ And the radius of the circle is 𝒓

26 EX: 1 Write the equation of the circle with a center at (3, –3) and a radius of 6. (x – h)2 + (y – k)2 = r 2 Equation of circle (x – 3)2 + (y – (–3))2 = 62 Substitution (x – 3)2 + (y + 3)2 = 36 Simplify. (x – 3)2 + (y + 3)2 = 36

27 You Try! Write the equation of the circle with a center at (2, –4) and a radius of 4. A. (x – 2)2 + (y + 4)2 = 4 B. (x + 2)2 + (y – 4)2 = 4 C. (x – 2)2 + (y + 4)2 = 16 D. (x + 2)2 + (y – 4)2 = 16

28 You Try Again! Write the equation of the circle graphed to the right.
A. x2 + (y + 3)2 = 3 B. x2 + (y – 3)2 = 3 C. x2 + (y + 3)2 = 9 D. x2 + (y – 3)2 = 9

29 You Try! Which of the following is the graph of x2 + y2 –10y = 0?
A. B. C. D.

Download ppt "All you need to know about Circles! By: Ms. Erwin"

Similar presentations

Lesson 10.1 Parts of a Circle Today, we are going to…

Lesson 10.1 Parts of a Circle Today, we are going to…
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.
Tangents, Arcs, and Chords

Tangents, Arcs, and Chords
CIRCLES 2 Moody Mathematics.

CIRCLES 2 Moody Mathematics.
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.
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.

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.
Chapter 11. If 2 sides of a triangle are radii then the triangle is ______________.

Chapter 11. If 2 sides of a triangle are radii then the triangle is ______________.
Circles Chapter 10.

Circles Chapter 10.
Circles.

Circles.
Ch 11 mini Unit. LearningTarget 11-1 Tangents I can use tangents to a circle to find missing values in figures.

Ch 11 mini Unit. LearningTarget 11-1 Tangents I can use tangents to a circle to find missing values in figures.
Unit 6 Day 1 Circle Vocabulary. In your pairs look up the definitions for your vocabulary words.

Unit 6 Day 1 Circle Vocabulary. In your pairs look up the definitions for your vocabulary words.
Tangents to Circles (with Circle Review)

Tangents to Circles (with Circle Review)
Circles. Vocabulary Interior Exterior Chord Secant.

Circles. Vocabulary Interior Exterior Chord Secant.
Lesson 8-1: Circle Terminology

Lesson 8-1: Circle Terminology
Β© T Madas O O O O O O O The Circle Theorems. Β© T Madas 1 st Theorem.

Β© T Madas O O O O O O O The Circle Theorems. Β© T Madas 1 st Theorem.
10.1 – Tangents to Circles. A circle is a set of points in a plane at a given distance from a given point in the plane. The given point is a center. CENTER.

10.1 – Tangents to Circles. A circle is a set of points in a plane at a given distance from a given point in the plane. The given point is a center. CENTER.
Circles Chapter 9. Tangent Lines (9-1) A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point. The.

Circles Chapter 9. Tangent Lines (9-1) A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point. The.
6.3 – 6.4 Properties of Chords and Inscribed Angles.

6.3 – 6.4 Properties of Chords and Inscribed Angles.
Circles Chapter 12.

Circles Chapter 12.
Circle Properties - Ch 6 Chord Central Angles Conjecture If two chords in a circle are congruent, then they determine two central angles that are…....congruent.

Circle Properties - Ch 6 Chord Central Angles Conjecture If two chords in a circle are congruent, then they determine two central angles that are…....congruent.

Similar presentations

Ads by Google