Chapter 10.3

Essential Question

What are the properties of chords?

What’s a chord again?

A chord is a segment inside a circle with endpoints on the circle.

Any chord will divide a circle into 2 arcs, a major and minor arc.

If there are any 2 chords of the same length, then their arcs are congruent.

What are the measures of arcs AB, AE, and BD? 360 – 75 – 75 = 210

210÷2 = 105

105º

105º

Find the measures of arcs AB and DB…Hint: they should be the same!

360 – 128= 232

232÷2 = 116

What do you know about the 2 segments?

3x + 7 = 4x

7 = x

Find x

5x - 6 = 2x + 93x - 6 = 93x = 15

x = 5

Find x

6x + 9 = 8x - 139 = 2x - 1322 = 2x 11 = x

The chords are congruent when they are the same distant from the center.

What do we know about the 2 segments?

5x - 7 = 185x = 25x = 5

If the 2 chords are congruent, what do we know about AQ and BQ?

4x + 1 = x + 83x + 1 = 83x = 7x = 2.333

Find the given arcIf the diameter is

perpendicular to a chord then it splits the chord in half.Find the other 2 arcs

A circle is 360º, so …

360 – 55 – 55 = 250

250 ÷ 2 = 125°

125° 12

5°

Find the missing arcs

If there are 4 arcs of equal size, what do you divide 360 by?

4

360 ÷ 4 = 90

Classzone eWorkbook 10.3