Circles and Arcs

Circles

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Circles Part 1

Basic Measurements

Radius - the distance from the center to the circle

Diameter - double the radius

Circumference - distance around the circle

Area - space inside the circle

Basic Calculations

Circumference - distance around the circle

Area - space inside the circle

Basic Calculations

Circumference - distance around the circle

Area - space inside the circle

Measurements

Arc Measure - the central angle of the arc

Arc Length - the distance from one point to another around the circle

Sector Area - Area inside the circle

Terms

Inscribed - a shape inside the circle with points on the circle

Inscribed Angle - is always half the size of the central angle

This means that the inscribed angle of a diameter is always a right angle

Other Notes

Every radius of a circle is the same length - this fact is used a lot and is often the key to answering the question.

A line tangent to a circle makes a 90^° angle with the radius.

Multiple Choice

• $$9$$

• $$12$$

• $$18$$

• $$36$$

Multiple Choice

• $$10$$  
  

• $$6$$  
  

• $$4$$  
  

• $$2$$  
  

Multiple Choice

• $$15$$  
  

• $$30$$  
  

• $$45$$  
  

• $$60$$  
  

Circles Part 2

Equation of a circle

Equation

Example

Hints

Be very careful with your SIGNS

Sketch out a grid so you can visuliaze what is going on

Multiple Choice

• $$\left(2,-5\right)$$

• $$\left(6,-1\right)$$

• $$\left(6,-5\right)$$

• $$\left(6,-9\right)$$

Fill in the Blanks