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Tangent and Chord Properties

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Presentation on theme: "Tangent and Chord Properties"— Presentation transcript:

1 Tangent and Chord Properties
Segments and Lines in relation to circles

2 Review of Terms and Ideas

3 Tangent Line or segment that touches a circle at one point ( point of tangency) This line or segment is perpendicular to the radius at this point

4 Tangent Segments Two segments tangent to a circle from the same point outside the circle are congruent. These lines would form an Isosceles Triangle, Why?

5 Tangent Circles Two circles that are tangent to each other, touch at only 1 point Internally Tangent – one circle inside the other Externally Tangent

6 Example

7 Example

8 Central Angle and Minor Arc
Central angle is the same as the arc it forms, formed by 2 radii at the center of the angle Minor arc is angle formed on the circle between the two radii, same as the central angle

9 Central Angle Has vertex at the center of the circle, both sides are radii of the circle

10 Chords Segment insides a circle, connecting two points on the circle Diameter is the longest chord in a circle

11 Inscribed Angles Vertex of angle is on the circle and sides are chords of the circle

12 Chord Central Angle If two chords in a circle are congruent, then they determine two central angles that are congruent

13 Chord Arcs If two chords in a circle are congruent, then their intercepted arcs are congruent

14 Chord Distance to Center
Two Congruent chords in a circle are equidistant to the center of the circle

15 Perpendicular to a Chord
The radius perpendicular to the chord will bisect the chord

16 Perpendicular Bisector of a Chord
The perpendicular bisector of a chord passes through the center of the circle

17 Examples

18 Examples

19 Terms Congruent Circles – same radius length Concentric Circles – same center different radii Radius – segment from center to any point on circle Chord – segment connecting any 2 points on circle Diameter- chord that goes through the center of the circle Tangent – segment or line that touches the circle at one point Central Angle – is the angle formed by 2 radii at the center of the circle Minor Arc – arc formed between 2 radii, measured in degrees Major Arc – larger arc formed by 2 radii Semicircle – half of a circle formed by diameter

20 HW Pg Pg Honors 11 and 12


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