Equation of a Circle 11/28/2023

​Lets start off with some review!

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Draw

Shade in what the circle would look like if we are trying to find the Area of a Sector for angle AQB?

Draw

Draw what the circle would look like if we are trying to find the Arc Length of AB ?

Draw

Circle the picture that goes along with the following question.

Find the length of arc AB when the diameter of circle C is 10 inches.

Multiple Choice

Find the length of arc AB when the diameter of circle C is 10 inches.

• 
  $$20\pi$$ in

• 
  $$2600\pi$$ in

• 
  $$\frac{12600\pi}{9}$$ in

• $$\frac{25\pi}{9}in$$

Fill in the Blank

Find the area of the shaded sector. Leave in terms of π.

(Leave pie out of your answer! Just type in the values. Imagine π at the end of the box.)

​Something new!!!

Multiple Choice

What is the center point for the following equation of a circle?

(x-h)²+(y-k)²=r²

(x-5)²+(y-3)²=r²

• (5,3)

• (-5,-3)

Multiple Choice

REMEMBER!!

Quadrilateral PQRT  is inscribed in a circle and the measure of ∠Q =54°.  What is the measure of ∠T ?

• 180⁰

• 54⁰

• 108

• 126⁰

Multiple Choice

What is the center point for the following equation of a circle?

(x-h)²+(y-k)²=r²

(x-7)²+(y-8)²=r²

• (7,8)

• (-7,-8)

Multiple Choice

What is the center point for the following equation of a circle?

(x-h)²+(y-k)²=r²

(x-8)²+(y+1)²=r²

• (8,-1)

• (-8,1)

Multiple Choice

What is the center point for the following equation of a circle?

(x-h)²+(y-k)²=r²

(x+8)²+(y-1)²=r²

• (8,-1)

• (-8,1)

Draw

Mark the center of the circle on the graph!

Draw

Mark the center of the circle on the graph!

Multiple Choice

REMEMBER!

Find the value of x in circle E.

• 52⁰

• 104⁰

• 26⁰

Multiple Choice

What is the radius in the following equation of a circle?

(x-h)²+(y-k)²=r²

(x-5)²+(y-4)²=9²

• 9

• 3

• 18

Multiple Choice

What is the radius in the following equation of a circle?

(x-h)²+(y-k)²=r²

(x-2)²+(y+7)²=4²

• 8

• 4

• 16

Multiple Choice

What is the radius in the following equation of a circle?

(x-h)²+(y-k)²=r²

(x-2)²+(y+7)²=25

• 25

• 5

• 12.5

Multiple Choice

What is the radius in the following equation of a circle?

(x-h)²+(y-k)²=r²

(x-7)²+(y+3)²=16

• 16

• 8

• 4

Draw

Mark the radius of the circle on the graph!

Draw

Mark the radius of the circle on the graph!

Multiple Choice

Write an equation if a circle has a center of (3, -1) and the diameter is 8.

(x-h)²+(y-k)²=r²

• (x-3)²-(y+1)²=4²

• (x-3)²+(y+1)²=4²

• (x-3)²+(y+1)²=8²

Multiple Choice

Write an equation if a circle has a center of (-2, 4) and the diameter is 4.

(x-h)²+(y-k)²=r²

• (x+2)²-(y-4)²=4

• (x+2)²+(y-4)²=4

• (x-2)²+(y+4)²=2

Multiple Choice

What is the length of the diameter of the circle defined by the equation (x − 5)²  + (y + 4)² = 144?

• d = 144

• d = 12

• d = 24

​Review from yesterday...

Intersecting Chords Theorem

Fill in the Blank

Solve for x

Tangent - Secant Theorem

Multiple Choice

Solve for x.

• 18

• 12

• 16

Secant-Secant Theorem

Multiple Choice

Solve for x.

• 12

• 1

• 4

External: angle=1/2(big arc - little arc)

When two secants meet outside of a circle, the angle is equal to half of the different of the arcs.

Fill in the Blank

What is the measure of the missing angle?

Internal: angle=1/2(big arc + little arc)

When two secants meet inside the circle, the angle is equal to half of the sum of the arcs.

Fill in the Blank

What is the measure of the internal angle?

Draw

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