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Circle Geometry

Circle Geometry. Tangents Points of Tangency Chords Inscribed Angles Central Angles Arcs. Review of Circle Terminology. Diameter- straight line that connects two points on a circle that passes through the centre of the circle.

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Circle Geometry

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  1. Circle Geometry Tangents Points of Tangency Chords Inscribed Angles Central Angles Arcs

  2. Review of Circle Terminology • Diameter- straight line that connects two points on a circle that passes through the centre of the circle. • Radius- straight line connecting the centre of the circle to the outer edge (circumference) • Circumference- outer edge of the circle (360 degrees)

  3. Tangent • A straight line that only intersects (touches) a circle at one point. • Easy to recognize due to it will always be located outside of the circle.

  4. Points of Tangency • The point where the tangent and circle intersect is called the point of tangency.

  5. Properties of Tangent/Points of Tangency • The tangent line is always perpendicular to the radius of the circle. (creates a right angle/90 degree angle) • ***

  6. Triangle Properties • 3 sided polygon. • All angles within a triangle add up to 180 degrees. • We can apply this principle to to solve for: • Angle from the centre of the circle to the tip of the tangent line. • Angle from the tip of the tangent line to the centre of the circle.

  7. Pythagoras Theorem • Formula? • What side is C? • Hypotenuse (opposite of the right angle. • What sides are A&B? • Two sides adjacent (beside) the right angle. • ***

  8. Application of Pyth to Tangents • Objective is to solve for the missing side using Pythagoras theorem. • Need to identify what side is missing and rearrange the formula to solve properly.

  9. Application of Pyth to Tangents • We can use Pythagoras Theorem to solve for the length of tangent lines, the length of the radius of a circle, and the distance between the end of a tangent line and the centre of the circle.

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