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

• $$\frac{25\pi}{9}in$$

​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

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.

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.

Draw

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