Tangent and Chord Properties Objective: Students will understand the terms related to circles and solve problems related to tangent lines and circles.

Review of Terms and Ideas

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

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?

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

Example

Example

Tangent Assignment Pg 313 1-5 and honors 7

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

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

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

Inscribed Angles Vertex of angle is on the circle and sides are chords of the circle Inscribed angles is half the measure of the intercepted arc

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

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

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

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

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

Examples

Examples

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

HW Pg 320 1-11 hon 15