Tuesday, February 5, 2013 Agenda: TISK, NO MM Lesson 9-3: Arcs & Chords HW Check (time) Homework: §9-3 problems in packet 12 34 56 7 8.

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Tuesday, February 5, 2013 Agenda: TISK, NO MM Lesson 9-3: Arcs & Chords HW Check (time) Homework: §9-3 problems in packet

§9-3 Arcs & Chords A B CD In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

Example Find the measure of each minor arc created when an equilateral triangle is inscribed in a circle. From yesterday, we know that

Theorem In a circle, if a diameter is perpendicular to a chord, then the diameter bisects the chord and its arc.

Example

Then we can use the Pythagorean Theorem to solve for x.

Example You discovered a crop circle in a nearby farm. A chord of the circle is 500 feet long and 600 feet from the center of the circle. Find the length of the radius to the nearest foot. 500 ft 600 ft ? Since the distance from a point (the center) to a segment (the chord) is always the length of the perpendicular segment, we know that the 600 ft segment bisects the 500 ft segment.

Theorem C D AB

C D AB E F G

Example Prove this condition of the theorem:  In a circle, if two chords are equidistant from the center, then they are congruent.

Homework Check Similar Congruent Concentric