Circles

Circles

By Amber Vrieze

Fill in the Blank

In circle Q, what is segment EQ?

Fill in the Blank

In circle Q, what is segment BD?

Fill in the Blank

In circle Q, what is segment AC?

Multiple Choice

The first Ferris wheel was built in 1893 in Chicago. Its diameter was 250 feet. About how many feet did the Ferris wheel rotate with one complete turn?

• 250 feet

• 500 feet

• 785 feet

• 1571 feet

Multiple Choice

A goat is tethered by a rope that is 3.5 m long. Find the maximum area that the goat can graze.

• $$22\ m$$  

• $$38.5\ m^2$$  

• $$153.9\ m^2$$  

• $$53.2\ m^2$$  

Multiple Choice

On a certain vehicle, one windshield wiper is 60 cm long. If the swing arm turns through 105°, what area of the windshield, to the nearest square centimeter, is swept by the wiper blade?

• $$3,299\ cm^2$$  

• $$11,310\ cm^2$$  

• $$825\ cm^2$$  

• $$7,562\ cm^2$$  

Multiple Choice

Shana is about to perform a relay handoff on a circular track that has a radius of 23 meters and her track partner Katie is standing 114° away from her. How many meters does Shana need to run to pass the baton to Katie? Round answers to the nearest meter.

• 23 m

• 46 m

• 72 m

• 145 m

Equation of a Circle

​(x - h)² + (y - k)² = r²

Where r is the radius of the circle and (h, k) is the center of the circle.

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Example: What is the equation for a circle with radius of 4 and centered at the point (-2, 3).

r = 4, h = -2 and k = 3

(x - (-2))² + ( y - 3)² = 4²

(x + 2)² + (y - 3)² = 16​

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​Click For Video

​https://watch.screencastify.com/v/Wrirdad9foeBYGRpHtgU

Equation of a Circle

​(x - h)² + (y - k)² = r²

Where r is the radius of the circle and (h, k) is the center of the circle.

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Example: Given the equation of a circle: (x - 4)² + (y + 5)² = 36, what is the center of the circle and its radius.

x - h = x - 4; so h = 4

y - k = y + 5; so k = -5

r² = 36; so r = √​36 and r = 6

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The circle is centerd at (4, -5) with a radius of 6​

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​Click for Video

​https://watch.screencastify.com/v/7NnOsAwV3qw2HXqlBc7Y

Multiple Choice

What is the equation for a circle centered at the origin with a radius of 3 cm.

• $$x^2+y^2=3$$  

• $$x^2-y^2=3$$  

• $$x^2+y^2=6$$  

• $$x^2+y^2=9$$  

Multiple Choice

A circle has equation $$\left(x-4\right)^2+y^2=25$$  , what is the radius of the circle?

• 5

• 4

• 0

• 25

Multiple Choice

What is the equation for this circle?

• $$\left(x\ +1\right)^2+\left(y+2\right)^2\ =4$$  

• $$\left(x-1\right)^2+\left(y-2\right)^2=4$$  

• $$\left(x-1\right)^2+\left(y-2\right)^2=2$$  

• $$x^2+y^2=2$$  

Multiple Choice

What is the equation for a circle centered at (-3, 0) and has a radius of 7 units.

• $$\left(x-3\right)^2+\left(y-1\right)^2=49$$  

• $$\left(x\ +\ 3\right)^2+y^2=7$$  

• $$x^2+\left(y-3\right)^2=7$$  

• $$\left(x+3\right)^2+y^2=49$$