Circles

Jed Butler, May 8, 2014

This collection demonstrates relationships with arcs, angles and segments found with circles (tangents, secants, and radii). There is also some applets related to partial circumference (arc length) and partial area of a circle (sector area).

Table of Contents

  1. Triangles (and Kites) with Circles
    1. Chords of Circle with Pythagorean Theorem applied to Kite
    2. Circle inscribed in Triangle With Tangents: Area & Perimeter
  2. Angle Relationships with Circles
    1. Angle And Arc Relationships
    2. Triangle Inside Circle
    3. Circle Angle Relationships: (Chord, Secant, Tangent)
    4. Secant Arcs and Angles in Circles
  3. Segments and Lines with Circles
    1. Circle Segment Relationships (Secant, Tangent, and Chord)
  4. Area and Circumference with Circles
    1. WYR Math #15 Pizza and Proportions of Circle Area
    2. Area and Circumference Proportions
    3. Circle unwrap 1

1.

Triangles (and Kites) with Circles

  • 1. Chords of Circle with Pythagorean Theorem applied to Kite
  • 2. Circle inscribed in Triangle With Tangents: Area & Perimeter

1.1.

Chords of Circle with Pythagorean Theorem applied to Kite

Chords of Circle with Pythagorean Theorem applied to Kite
1) What shapes do you see inside of the kite?[br]2) How can you find [br]-2a. the green lengths?[br]-2b. CD?
– Jed Butler

1.2.

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2.

Angle Relationships with Circles

  • 1. Angle And Arc Relationships
  • 2. Triangle Inside Circle
  • 3. Circle Angle Relationships: (Chord, Secant, Tangent)
  • 4. Secant Arcs and Angles in Circles

2.1.

Angle And Arc Relationships

Use the slider to adjust the angle measures.
Angle And Arc Relationships
1) Which angles make a straight angle?[br][br]2) Which angles make a right angle?[br][br]3) Which angles are congruent?[br][br]How do you know?
– Jed Butler

2.2.

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2.3.

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2.4.

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3.

Segments and Lines with Circles

  • 1. Circle Segment Relationships (Secant, Tangent, and Chord)

3.1.

Circle Segment Relationships (Secant, Tangent, and Chord)

Can you make point C move 1) inside the circle; 2) on the circle (try to get L and K to overlap); 3) outside the circle?[br][br]Also try to make an equation using the measures you're given.
What do you notice?[br][br][br][br][br]What do you wonder?
– Jed Butler

4.

Area and Circumference with Circles

  • 1. WYR Math #15 Pizza and Proportions of Circle Area
  • 2. Area and Circumference Proportions
  • 3. Circle unwrap 1

4.1.

WYR Math #15 Pizza and Proportions of Circle Area

Use the sliders to create two different combinations of pizza. Can you create a pair of combinations that are approximately (or even exactly) equal?
WYR Math #15 Pizza and Proportions of Circle Area
– Jed Butler

4.2.

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4.3.

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