Warm UpApr. 24 th 1.The perimeter of an equilateral triangle is 36 inches. Find the length of an altitude. Give the exact answer (in simplified radical form). 2. a = ____ 3. b = ____ x 4. Find the exact value of x.

Homework Check/Questions??

Tangents & Chords Thurs. Apr. 24 th

A circle is the set of all points in a plane at a given distance (radius) from a given point (center) in the plane. Congruent circles – Concentric circles -

Chord – Secant - Tangent line(segment) -

a. Draw a tangent line and a radius to the point of tangency. b. Describe the relationship between the tangent line and the radius of the circle drawn to the point of tangency.

is tangent to the circle. x = ____

is tangent to  C. What is the radius of the circle?

m  OJT = 30º, JO = 20, then JT = ______ JK = 9, KO = 8, then JT = ______

Theorem: The tangent segments to a circle from a point outside the circle are congruent. How do you know?

Example: In the diagram, RT = 12 cm, RH = 5 cm, and MT = 21 cm. Determine the length of.

In the circle: Draw a diameter. Draw a chord that is perpendicular to the diameter. What appears to be true of a chord perpendicular to a diameter?

Example: A chord of a circle is 12 in. long, and its midpoint is 8 in. from the center of the circle. Calculate the length of the radius of the circle.

Theorem: In a circle (or congruent circles), two congruent chords are equidistant from the center of the circle. RS = ______

1) 2) 3) 4)

Angles and Arcs Vocab & Chart Start Thurs. Apr. 24 th & Finish Fri. Apr. 25 th

An arc is an unbroken part of a circle. Minor Arc -less than half of the circle Semi-circle- exactly half of the circle Major Arc -more than half of the circle. Three types of arcs…

A central angle of a circle is an angle with its vertex at the center of the circle. Type of angle Where is the vertex? Example Description of angle measurement Formula for measure using example Central Angle

An inscribed angle is an angle whose vertex is on the circle and whose sides contain chords of the circle.

Type of angle Where is the vertex? Example Description of angle measurement Formula for measure using example Inscribed Angle Formed by tangent and chord

“inside” angle… “ Inside ” angle Type of angle Where is the vertex? Example Description of angle measurement Formula for measure using example

“outside” angles

Examples

Find the measure of each arc.

Angle formed by a chord (or secant) and tangent…

You Try!

Any angle inscribed in a semi-circle is a _____ angle. If a quadrilateral is inscribed in a circle, then the opposite angles are supplementary.

…and the special note

Quiz Day!Apr. 28 th 1)Clear your desk except something to write with and a calculator. 2)Please leave answers in simplified radical form, no rounded decimals! 3)When finished, please turn it in on the cart and check your homework answers.

Homework Check & Questions?

Mon. Apr. 28 th

Lance owns The Flyright Company. His company specializes in making parachutes and skydiving equipment. After returning from a tour of Timberlake Gardens, he was inspired to create a garden in the circular drive in front of his office building. Lance decided to hire a landscape architect to design his garden. The architect told Lance that he would need to determine the area and circumference of the garden. 1.What formula can be used to determine the circumference of the circle? What information does the circumference provide about the garden? 2.What formula can be used to determine the area of the circle? What information does the area provide about the garden?

The layout of The Flyright Company’s building and parking lot are shown. 3.What is the radius, circumference and area of the largest circle that will fit in the grassy area? Justify your answer. Give your answers in π form then round each to 1 decimal place.

4.Lance decides he would like the garden to have a circumference of 40π feet. What would be the area of this garden? 5.If the area of the garden needs to be 225 π feet, what would be the circumference?

6.Lance is also considering including a sidewalk around the outside of the garden, as shown below. Determine the area of the sidewalk.

Lance would like his garden to resemble a colorful parachute with different flowers in alternating areas of the garden. His sketch for the landscaper is shown below. The circle garden is divided into 8 equal parts (called sectors). a)What portion of the total area of the circle is each part? Recall that Lance would like the diameter of his circle garden to be 20 feet. b) Determine the area of each sector of the garden. c) Determine the arc length of each sector of Lance’s garden.

Mrs. Little boards a Ferris wheel with a diameter of 100 feet. Calculate the approximate distance that Mrs. Little traveled in her 6 revolutions. Round to 3 decimal places.

Use circle B below to answer the following: a)Area: b)Area of Shaded Sector: c)Circumference: d)Length of AC:

Examples The length of an arc in a circle with radius 8 inches is 3.2π inches. Determine the measure of the arc. The measure of the central angle of a sector is 60° and the area of the sector is 6π inches. Calculate the radius of the circle.

Warm Up Apr. 29 th 1)Find the midpoint and distance of (-3, 6) and (7, 11) 2)Expand and simplify: (x – 3) 2 3)Factor: x 2 + 8x )Solve by completing the square: x 2 – 4x + 10 = 31

Homework Check & Questions?

Tues. Apr. 29 th

Revisit the definition…. A circle is the set of all points in a plane that are equidistant from a given point.

Write the equation of the circle described … Center (0, 3) and radius = 5 Center (-4, 5) and radius = 7

Write the equation of the circle described … Center (2, -1) and contains the point (0, 4) Endpoints of the diameter (-1, 3) and (5, 1)

Write the equation of the circle described … Contains the three points (2, 4), (6, 2), and (-1, -5) More Circles

Identify the center and radius of the circle (x – 3) 2 + (y + 1) 2 = 49 x 2 + (y – 5) 2 = 10

What would this equation look like if we expanded the binomials…. (x – 3) 2 + (y + 1) 2 = 49 x 2 + (y – 5) 2 = 10

Rewrite the equation in information form and identify the center and radius of the circle x 2 + y 2 – 6x + 2y = 6 x 2 + y 2 + x + 4y = 0

Determine the area and circumference of the circle whose equation is: (x – 3) 2 + y 2 = 12 x 2 + y x + 8y = 8

Given circle O with equation x 2 + y 2 – 8y + 7 = 0 Rewrite the equation in information form. Determine the center and radius of the circle. Determine whether each point below is in the interior, exterior or on the circle. –(5,-2) –(0,7) –(1, 3)

Warm UpApr. 30 th 1.Given points (-5, 2) and (-1, 6) are the endpoints of a diameter of a circle. Write the equation of the circle. 2.Determine the center and radius of the circle: x 2 + y 2 – 6x – 10y = 2 3.QR = ____ 4.QP = ____ 5.TP = ____

Quadratic Functions as Conics Wed. Apr. 30 th

Homework Check & Questions?

y = ¼x 2 Look at the point F(0, 1) and the line y = -1. What do you notice about the distance from F to the vertex and the distance from the line y = -1 to the vertex? What is the vertex?

A parabola is the set of all points that are equidistant from a fixed point, called the focus, and a fixed line called the directrix. A focus and directrix uniquely determine a parabola.

In general, if the distance from the vertex to the focus (or directrix) is c and the vertex is (h, k), the equation in information form is __________________________________

A parabola with focus F(2, 4) and directrix y = -2. What are the coordinates of the vertex of the parabola? What is the equation for the parabola in information form?

Identify the coordinates of the vertex, coordinates of the focus and equation of the directrix.

Identify the coordinates of the vertex, coordinates of the focus and equation of the directrix.

Examples: Write the equation of the parabola.

Write the equation of the parabola with vertex (2, -3) and directrix y = -5

Warm UpMay 1 st 1.Rewrite the equation in information form, identify the center and radius: x 2 + y 2 + 8x – 6y = 1 2.Graph the circle: (x – 1) 2 + y 2 = 9 3.Determine the focus and directrix y = -3(x + 1) 2 - 4

Review Day