10.3 Chords. Review Draw the following on your desk. 1)Chord AB 2)Diameter CD 3)Radius EF 4)Tangent GH 5)Secant XY.

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Presentation transcript:

10.3 Chords

Review Draw the following on your desk. 1)Chord AB 2)Diameter CD 3)Radius EF 4)Tangent GH 5)Secant XY

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

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

Open a new Geogebra File 1)Construct a circle A through point B. 2)Construct a chord BC. 3)Construct a perpendicular bisector of chord BC. 4)What do you notice? 5)Adjust the size of the circle, is the hypothesis you made in step (4) still true?

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

Open a new Geogebra File 1)Construct a circle A through point B. 2)Construct a chord BC. 3)Construct a perpendicular line (not bisector, just perpendicular) through the center A and perpendicular to chord BC. 4)Construct point D on the intersection of the perpendicular line and chord BC. 5)Construct a circle with center D through point B. 6)What type of segment is AD?

Perpendicular to a Chord Conjecture The perpendicular from the center of a circle to a chord is the bisector of the chord.

Chord Distance to Center Conjecture Two congruent chords in a circle are equidistant from the center of the circle. Let’s prove it…

Two congruent chords in a circle are equidistant from the center of the circle.

Guided Practice Find the measure of arc YX Find x.