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Arcs and Chords

Arcs and Chords. Section 10.3. Vocabulary. Inscribed polygon – a polygon where all vertices lie on the circle Not inscribed. Circumscribed - a circle is circumscribed about a polygon when it contains all of the vertices of the polygon. Ex. 2

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Arcs and Chords

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  1. Arcs and Chords Section 10.3

  2. Vocabulary • Inscribed polygon – a polygon where all vertices lie on the circle • Not inscribed

  3. Circumscribed - a circle is circumscribed about a polygon when it contains all of the vertices of the polygon

  4. .

  5. Ex. 2 • A circle is circumscribed about a regular pentagon. What is the measure of the arc between each pair of consecutive vertices? • A. 60 B. 72 C. 36 D. 30

  6. Theorem 10.3

  7. Ex. 3 Circle O has a radius of 13 in. Radius is perpendicular to chord, which is 24 inches long. • A. If , find • bisects

  8. B. Find OX • is a right triangle with CO = 13 • bisects so CX = 12 • Use Pythagorean Theorem to find OX. • 122 + OX2 = 132 • OX = 5

  9. Circle R has a radius of 16 cm. Radius is perpendicular to chord which is 22 cm. • A. if , find • B. Find RS

  10. Ex 4 • Chords and are equidistant from the center. If the radius of circle G is 26, find AC and DE. • Since AC and DF are equidistant from G then • and are radii and form 2 right triangles. Use the Pythagorean theorem to solve for AB. • AB = 24 • AC = 48 so DF = 48 and DE = 24

  11. Chords and are equidistant from the center. If the radius of circle S is 15, find MO and PQ.

  12. The radius of a circle is 22 cm and a chord is 40 cm. How far is the chord from the center of the circle?

  13. A chord of a circle is 50 in. and 12 in from the center of a circle. Find the radius.

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