Review Tangents, plus Arcs, Central Angles and Chords

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Presentation transcript:

Review Tangents, plus Arcs, Central Angles and Chords May 9, 2008

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problems 6 and 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Central Angles

What is an arc?

Measure of a minor arc

What is a major arc?

Measure of a major arc In the next diagram we see that the measure of a major arc is 360 minus the measure of its associated minor arc.

Semicircles

Adjacent Arcs Adjacent arcs of a circle are arcs that have exactly one point in common. Arc AC and arc CB are adjacent arcs since they share only the point C.

Arc Addition Postulate Arc Addition Postulate: The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.

Congruent Arcs Congruent arcs are arcs, in the same circle or in congruent circles, that have equal measures.

Chords In the diagram below, chord AB cuts off two arcs, arc AB and arc ATB. We call AB the minor arc, the arc of chord AB.

More about chords Theorem: In the same circle or congruent circles: (1) Congruent arcs have congruent chords (2) Congruent chords have congruent arcs.

Even more about chords.. Theorem: A diameter that is perpendicular to a chord bisects the chord and its arc.

Just a little bit more Theorem: In the same circle or in congruent circles: (1) Chords equally distant from the center (or centers) are congruent. (2) Congruent chords are equally distant from the center (or centers).