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C I R CL E S

Circle - a set of points equidistant from a given point called the center. C I R CL E S. Circle - a set of points equidistant from a given point called the center. C I R CL E S. RADIUS. Radius – the distance from the center to any point on the edge of the circle.

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C I R CL E S

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  1. Circle - a set of points equidistant from a given point called the center C I R CL E S

  2. Circle - a set of points equidistant from a given point called the center C I R CL E S RADIUS Radius – the distance from the center to any point on the edge of the circle

  3. Circle - a set of points equidistant from a given point called the center C I R CL E S DIAMETER Radius – the distance from the center to any point on the edge of the circle Diameter – the distance from one side of the circle to the other thru the center

  4. Circle - a set of points equidistant from a given point called the center C I R CL E S DIAMETER

  5. Circle - a set of points equidistant from a given point called the center C I R CL E S

  6. Circle - a set of points equidistant from a given point called the center C I R CL E S

  7. Circle - a set of points equidistant from a given point called the center C I R CL E S Tangent Line – a line that intersects a circle at a single point

  8. Circle - a set of points equidistant from a given point called the center C I R CL E S Tangent Line – a line that intersects a circle at a single point A tangent line creates a 90 degree angle with the radius…

  9. Circle - a set of points equidistant from a given point called the center C I R CL E S B A

  10. C I R CL E S C B A When a circle is divided by a pair of radii into two unequal parts, it creates two arcs.

  11. C I R CL E S C B A When a circle is divided by a pair of radii into two unequal parts, it creates two arcs. Arc ACB is called a “major” arc.

  12. C I R CL E S C B A When a circle is divided by a pair of radii into two unequal parts, it creates two arcs. Arc ACB is called a “major” arc. Arc AB is called a “minor” arc,

  13. C I R CL E S W Central angle B A When two radii create an angle, it is called a central angle.

  14. C I R CL E S W Central angle B A When two radii create an angle, it is called a central angle. The arc created has the same measure as the angle.

  15. C I R CL E S W B A When two radii create an angle, it is called a central angle. The arc created has the same measure as the angle. For example, if angle AWB = 40 degrees. arc AB = 40 degrees

  16. C I R CL E S W B A A line segment whose endpoints lie on the circle is called a chord.

  17. C I R CL E S W B A A line segment whose endpoints lie on the circle is called a chord. Segments AW and BW create an angle.

  18. C I R CL E S W B A A line segment whose endpoints lie on the circle is called a chord. Segments AW and BW create an angle. When an angle is created whose vertex lies on the edge of a circle, it is called an “inscribed angle”.

  19. C I R CL E S W B A A line segment whose endpoints lie on the circle is called a chord. Segments AW and BW create an angle. When an angle is created whose vertex lies on the edge of a circle, it is called an “inscribed angle”. Angle AWB is an inscribed angle.

  20. C I R CL E S W B A A line segment whose endpoints lie on the circle is called a chord. Segments AW and BW create an angle. When an angle is created whose vertex lies on the edge of a circle, it is called an “inscribed angle”. Angle AWB is an inscribed angle. The arc it intercepts will always be 2 times the measure of the angle.

  21. C I R CL E S W B A A line segment whose endpoints lie on the circle is called a chord. Segments AW and BW create an angle. When an angle is created whose vertex lies on the edge of a circle, it is called an “inscribed angle”. Angle AWB is an inscribed angle. The arc it intercepts will always be 2 times the measure of the angle. So if angle AWB = 25 degrees…

  22. C I R CL E S W B A A line segment whose endpoints lie on the circle is called a chord. Segments AW and BW create an angle. When an angle is created whose vertex lies on the edge of a circle, it is called an “inscribed angle”. Angle AWB is an inscribed angle. The arc it intercepts will always be 2 times the measure of the angle. So if angle AWB = 25 degrees… arc AB = 50 degrees.

  23. Some example problems with circles. C I R CL E S A Q O B Example # 1 : If arc AB = 3 cm, and the circumference of the circle = 9 cm, what is the measure of the central angle ?

  24. Some example problems with circles. C I R CL E S A Q O B Example # 1 : If arc AB = 3 cm, and the circumference of the circle = 9 cm, what is the measure of the central angle ? Solution : all circles contain 360 degrees.

  25. Some example problems with circles. C I R CL E S A Q O B Example # 1 : If arc AB = 3 cm, and the circumference of the circle = 9 cm, what is the measure of the central angle ? Solution : all circles contain 360 degrees. - we can use a proportion to solve the problem

  26. Some example problems with circles. C I R CL E S A Q O B

  27. Some example problems with circles. C I R CL E S A Q O B

  28. Some example problems with circles. C I R CL E S A Q O B

  29. Some example problems with circles. C I R CL E S A Q O B

  30. Some example problems with circles. C I R CL E S A Q O B What we found was the measure of arc AB in degrees…

  31. Some example problems with circles. C I R CL E S A Q O SO the central angle AOB must also = 120 degrees…… B What we found was the measure of arc AB in degrees…

  32. Some example problems with circles. C I R CL E S A B E D C Example # 2 : If AE = 8.5 mm, BE = 17 mm, and CE = 12mm, what is the measure of line segment DE ?

  33. Some example problems with circles. C I R CL E S A B E D C Example # 2 : If AE = 8.5 mm, BE = 17 mm, and CE = 12mm, what is the measure of line segment DE ?

  34. Some example problems with circles. C I R CL E S A B E D C

  35. Some example problems with circles. C I R CL E S A B E D C

  36. Some example problems with circles. C I R CL E S A B E D C

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