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Solve the equations

Solve the equations. 3x=x+50 y+5y+66=360 x+14x=180 a 2 +16=25. Note: A diameter is a chord but not all chords are diameters. 10.2 ARCS AND CHORDS. An arc is a portion of the circumference of a circle. A chord is a line segment drawn between the end points of the arc. minor arc. chord.

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Solve the equations

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  1. Solve the equations • 3x=x+50 • y+5y+66=360 • x+14x=180 • a2+16=25 Note: A diameter is a chord but not all chords are diameters

  2. 10.2 ARCS AND CHORDS

  3. An arc is a portion of the circumference of a circle. • A chord is a line segment drawn between the end points of the arc minor arc chord major arc

  4. Two Ways To Measure Arcs: • central angle: in degrees • the length of the arc: in radians

  5. Measure of minor arc = measure of central angleMeasure of major arc = 360 – central angle C radius minor arcs AC CB central angle Major arcs ABC CAB chord A B center diameter O Semicircle ACB

  6. Postulate 26- Arc Addition Postulate • The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. mABC = mAB + mBC

  7. Theorem 10.4 • If the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

  8. Are the arcs congruent? 1. Arcs AB and CD 2. Arcs XY and ZW yes No

  9. Theorem 10.5 • If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.

  10. Theorem 10.6 • If one chord is a perpendicular bisector of another chord, then the first chord is a diameter.

  11. Theorem 10.7 • In the same circle, or in congruent circles, two chords are congruent iff they are equidistant from the center.

  12. Practice Time! • Find the measure of each arc of ⨀A. • BD • BE • BED 1250 1370 2350

  13. Find mBC. How to locate the center of the following circle using the chords shown. 1220

  14. AB=12, DE = 12, and CE= 7. Find CG.

  15. The graph shows the percent of each type of bicycle sold in the U.S. in 2001 Find the measurement of the central angle representing each category. List them from least to greatest. 25.20,32.40, 75.60, 93.60, 133,20

  16. What is the arc measure when the minute hand on a clock move in 10 minutes? How far will the tip of a 14cm long minute hand travel? • ≈14.66 cm

  17. Which is closer to the center of a circle? A longer chord or a shorter chord? Explain.

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