Unit 14 - Circles

Question 1

Definition of Congruent Circles (2)

Answer 1

1. Circles with different centers but same radii
2. Two circles with ≅ radii are ≅

Question 2

Definition of Central Angle (2)

Answer 2

1. Angle with a vertex AT THE CENTER OF CIRCLE
2. Measure of Central Angle = MEASURE of Intercepted Arc

Question 3

Definition of Concentric Circles

Answer 3

Circles with same centers but different radii

Question 4

Definition of Semi - Circle

Answer 4

180 Degree Arc

Question 5

Definition of Inscribed Angle (3)

Answer 5

1. Vertex meets circle & sides are chords
2. Ins ∠ ≅ to 1/2 int arc
3. Inscribed ∠s are ≅ when intercepting same arc

Question 6

Formula for Arc Length (2)

Answer 6

1. ℒ /2πr = X/360
2. Arc length - Circumference Ratio = Arc Measure - 360 Ratio

Question 7

Formula for Arc Area (2)

Answer 7

1. As/πr² = X/360
2. Sector Area - Circle Area = Sector Measure - 360 Ratio

Question 8

Definition of Thales’ Theorem

Answer 8

If inscribed ∠ of △ int. diameter/semicircle, ∠ is rt

Question 9

What is the Congruent Arc Theorem? (2)

Answer 9

Arcs are ≅ when sharing same/≅ CA

Question 10

What is the Arc & Chords Theorem? (4)

Answer 10

1. ≅ arcs have ≅ chords
2. ≅ CA have ≅ chords
3. Arcs between parallel chords are ≅
4. Chords are ≅ when ⊥ equidistant from center

Question 11

What is the Bisecting Arcs & Chords Theorem?

Answer 11

Diameter ⊥ to chord, bisects chord/minor arc/major arc

Question 12

What can you do to form a right triangle when utilizing the Bisecting Arcs & Chords Theorem?

Answer 12

You can draw your own radii to form a right triangle

Question 13

How can equidistance help you in solving circle diagrams?

Answer 13

Two chords are ≅ when ⊥ equidistant from center

Question 14

Definition of Tangent (4)

Answer 14

1. Line that intersects circle at ONE point
2. This single point is the point of tangency
3. WILL ALWAYS/MUST BE ⊥ TO RADIUS
4. Common tangent - Tangent to two circles

Question 15

Tangent Theorems (2)

Answer 15

1. Tangent must be ⊥ to radius drawn to point of tangency
2. Two tangents from the same exterior point are ≅

Question 16

How to construct a Tangent (5)

Answer 16

1. Draw radius on circle
2. Label point of tangency
3. Extend radius
4. Draw circle around point of tangency
5. Using new endpts, draw ⊥ bisector

Question 17

Definition of Inscribed Polygon (in relation to circle)

Answer 17

Polygon is inscribed (INSIDE) circle

Question 18

Definition of Circumscribed Polygon (in relation to circle)

Answer 18

Circle is inscribed (INSIDE) polygon

Question 19

How do the rules of tangents apply to a circumscribed polygon? (2)

Answer 19

1. bc sides of polygon touches circle, it’s a tangent
2. At vertices, ICC applies to each 0.5 tangents

Question 20

How to draw inscribed circle (5)

Answer 20

1. Reflect center over side of polygon
2. Draw arc, and draw arcs from both endpts
3. Draw line from intersection of arcs to center
4. Label point of line intersection to polygon side
5. Draw circle using center & labeled point

Question 21

How do you write equations of tangent lines? (2)

Answer 21

1. Find m of radius & ⊥m is slope of tangent
2. Plug slope & POT coordinates to y - k = m (x - h)

Question 22

Definition of Secant

Answer 22

A line that intersects a circle at two points

Question 23

Definition of Floating Angles (2)

Answer 23

1. Angles in a circle that is not inscribed or a central angle
2. Formed by the intersection of two chords/two secants

Question 24

How do you find the measure of a floating angle? (2)

Answer 24

1. Average of the arcs
2. 1/2 of the sum of arcs intercepted by two secants/chords

Question 25

What is formed when a secant and tangent intersect at the point of tangency? (3)

Answer 25

1. Forms an "inscribed" angle (part of it is in the circle, some isn't, but vertex is on the circle) 2. Measure of the angle is one half the measure of intercepted arc 3. To identify, it was to be bc of the INTERSECTION OF SECANT AND TANGENT

Question 26

What is an exterior angle in context of a circle? (5)

Answer 26

1. If two secants/a secant & a tangent/two tangents intersect 2. At an exterior point (in relation to a circle) 3. An exterior angle is formed 4. These lines also intercept TWO arcs 5. Measure of exterior angle = (int. big arc - int. little arc)/2

Question 27

What are the theorems relating to similar triangles?

Answer 27

- 2 Chord Intersection - (Part) (Part) = (Part) (Part) - 2 Secants (Exterior ∠) - (Whole) (Out) = (Whole) (Out) - Tangent & Secant - (Whole) (Out) = (Tan)

Question 28

Center - Radius Formula for Circle (2)

Answer 28

1. (h,k) - Coordinates for Center, r = Radius 2. (x - h)² + (y - k)² = r²

Question 29

Midpoint Formula

Answer 29

M = (x₁ + x₂) / 2, (y₁ + y₂) / 2)

Question 30

Distance Formula

Answer 30

d = √(x₂ - x₁)² + (y₂ - y₁)²