T4U1 - Equation of a Circle Plus Reteach/Spiral Review

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​T4U1 - Reteach

Parts of a Circle and Circumference

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You will be reviewing the parts of a circle needed for finding the circumference.

What is a Circle?

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A circle is a set of all points equidistance from on point called the center.

Circles are named by their center.

The circle to the right is ⊙O.

Parts of a Circle

Multiple Choice

14cm in the circle represents its

• radius

• diameter

Fill in the Blanks

Fill in the Blanks

​Circumference

 ​Circumference - the distance around a circle.

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C = πd C = 2πr

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​​Where d is the diameter and r is the radius.

Value of Pi

Pi is the ratio of the circumference to the diameter of a circle.

It is an irrational number, so we use the symbol "π​."

Sometimes it is necessary to round pi.

π ​≈ 3.14

When possible, use the pi button on your calculator. ​

Finding Circumference given radius

Finding Circumference given diameter

Multiple Choice

Find the circumference of the circle

• 50.24 yd

• 25.12 yd

• 11.14 yd

Multiple Choice

Find the circumference of the circle

• 18.84 cm

• 75.36 cm

• 37.68 cm

Multiple Choice

Find the circumference of the circle whose radius is 4 in

• 12.56 in

• 25.12 in

• 50.24 in

Multiple Choice

Find the circumference of the circle whose diameter is 10 m

• 31.4 m

• 62.8 m

• 15.7 m

Intro to Arc in a cirlce

Remember a circle has 360 degrees and a portion of a circle is called an arc, which looks like the crust of a slice of pizza. There are three types of arcs called minor, major, and semicircle.

Multiple Choice

How many degrees does a circle have?

• less than 180

• equal to 180

• more than 180

• 360

Arc Labels

• A minor arc is labeled with 2 letters, for example AX

• A major arc is labeled with 3 letters, for example AXY.

• A semicircle is labeled with 3 letters, for example XBY.

Multiple Choice

How many degrees does a major arc have?

• less than 180

• equal to 180

• more than 180

• 360

Multiple Choice

How many degrees does a semicircle have?

• less than 180

• equal to 180

• more than 180

• 360

Multiple Choice

How many degrees does a minor arc have?

• less than 180

• equal to 180

• more than 180

• 360

Multiple Select

Check all that is true about the Arcs in the circle

• XB is a Major Arc

• XAY is a semicircle

• XYA is a Major Arc

• XB is a semicircle

Things to know as we find the measure of an Arc.

• There are 360 degrees in a circle

• There are 180 degrees in a semicircle

• A diameter is a line that goes though the center of a circle splitting it into two semicircles.

• A central angle is where two radii form an angle with the vertex at the center of a circle.

• The measure of the arc formed by a central angle is equal to the measure of the central angle

Multiple Choice

A ____ angle is an angle whose vertex is a the center of a circle.

• supplementary

• complimentary

• central

• obtuse

Multiple Choice

What is the value of x?

• x = 160

• x = 40

• x = 80

• x = 360

Multiple Choice

What is the measure of arc AB?

• 140

• 142

• 180

• 153

Multiple Choice

Find the measure of Arc TW.

• 319º

• 41º

• 360º

• 82º

Inscribed Angles & Intercepted Arcs

Inscribed Angles

Here are some NON-examples. These are NOT inscribed angles.

Inscribed Angles vs. Central Angles

Multiple Choice

What is the measure of arc PR ?

• 360º

• 45º

• 90º

• 180º

Inscribed Angles vs. Central Angles

Open Ended

In general, what can you tell about the measure of

$$\angle PQR$$  compared to central angle $$\angle POR$$  

Take a look at this animation similar to our Circle O

Inscribed Angles have a measure that is exactly HALF of the measure of their intercepted arc.

Multiple Choice

What is the measure of

$$\angle EDF$$  ? (click image to enlarge)

• 120º

• 60º

• 180º

• 360º

Multiple Choice

What is the measure of

$$\angle XWE$$  ? (click image to enlarge)

• 180º

• 112º

• 56º

• 360º

Multiple Choice

Find the measure of the

$$arc\ \overline{DC}$$  . (click image to enlarge)

• 124º

• 62º

• 31º

• 360º

Multiple Choice

Find the measure of the

$$arc\ \overline{XW}$$ . (click image to enlarge)

• 56º

• 180º

• 360º

• 106º

Equations of Circles

From the Equation

• Make the signs on h and k OPPOSITE to get the center

• Take the SQUARE ROOT of r² to get the radius

• If you don't see an h or k, then that means the coordinate is (0,0).

Multiple Choice

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

• (3,2)

• (-3, -2)

• (-2, -3)

• (2, 3)

Multiple Choice

In the equation (x-3)²+(y-2)²=16, the radius of the circle is...

• 16

• 32

• 8

• 4

Multiple Choice

In the equation x²+(y+5)²=10, what is the center?

• (1, 5)

• (-1, -5)

• (0, 5)

• (0, -5)

To Write the Equation

• Write the formula/equation.

• Plug in what you know.

  • WHATCH YOUR SIGNS​

  • If you were given the diameter, then divide that by 2 to get the radius. And plug that in.

• Simplify

Multiple Choice

The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.

• (x - 2)² + (y + 5)² = 36

• (x - 5)² + (y + 2)² = 6

• (x + 5)² + (y - 2)² = 36

• (x + 2)² + (y - 5)² = 6

Multiple Choice

Write the equation of a circle with center (7, 0) with radius 3.

• (x - 7)² + y² = 9

• x² + (y -7)² = 9

• (x - 7)² + y² = 3

• x² + (y -7)² = 3

From a Graph

• Find the coordinates of the center. Make the signs on both of them OPPOSITE before you plug them in for h and k.

• Find the radius by counting the distance from the center out to the edge of the circle. Then SQUARE that before you plug it in for r²

Multiple Choice

What is the equation for this circle?

• (x+1)²+(y+1)²=9

• x²+y²=9

• x²+y²=6

• x²+y²=3

Multiple Choice

What is the equation of the circle?

• (x+1)² + (y +1)² = 3

• (x+1)² + (y -1)² = 3

• (x+1)² + (y +1)² = 9

• (x-1)² + (y -1)² = 9