5-Minute Check on Lesson 10-2 Transparency 10-3 Click the mouse button or press the Space Bar to display the answers. In ⊙ O, BD is a diameter and m 

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Presentation transcript:

5-Minute Check on Lesson 10-2 Transparency 10-3 Click the mouse button or press the Space Bar to display the answers. In ⊙ O, BD is a diameter and m  AOD =55°. Find each measure. 1.m  COB 2.m  DOC 3.m  AOB Refer to ⊙ P. Find each measure. 4. mLM 5. mMOL 6. If the measure of an arc is 68°, what is the measure of its central angle? Standardized Test Practice: ACBD 34° 68°102°136° 125° 114° 66° 150° 210° B

Lesson 10-3 Arcs and Chords

Objectives Recognize and use relationships between arcs and chords Recognize and use relationships between arcs and diameters

Vocabulary Inscribed Polygon – all vertices lie on the circle Circumscribed – circle contains all vertices of a polygon

Example 3-2a TESSELLATIONS The rotations of a tessellation can create twelve congruent central angles. Determine whether. Answer: Since the measures of are equal,. Because all of the twelve central angles are congruent, the measure of each angle is 360  12 or 30 Let the center of the circle be A. The measure of  PAQ is 5 30 or 150. Then. The measure of  SAT is 5 30 or 150. Then.

Example 3-2c ADVERTISING A logo for an advertising campaign is a pentagon that has five congruent central angles. Determine whether. Answer: no

Example 3-3a Circle W has a radius of 10 centimeters. Radius is perpendicular to chord which is 16 centimeters long. If find Since radius is perpendicular to chord Answer: 127

Example 3-3c Circle W has a radius of 10 centimeters. Radius is perpendicular to chord which is 16 centimeters long. Find JL. A radius perpendicular to a chord bisects it. Definition of segment bisector Draw radius 

Example 3-3e Use the Pythagorean Theorem to find WJ. Pythagorean Theorem Simplify. Subtract 64 from each side. Take the square root of each side. Segment addition Subtract 6 from each side. Answer: 4

Example 3-3g Answer: 145 Answer: 10 Circle O has a radius of 25 units. Radius is perpendicular to chord which is 40 units long. a. If b. Find CH.

Example 3-4a Chords and are equidistant from the center. If the radius of is 15 and EF = 24, find PR and RH. are equidistant from P, so.

Example 3-4c Draw to form a right triangle. Use the Pythagorean Theorem. Pythagorean Theorem Simplify. Subtract 144 from each side. Take the square root of each side. Answer:

Example 3-4d Answer: Chords and are equidistant from the center of If TX is 39 and XY is 15, find WZ and UV.

Summary & Homework Summary: –The endpoints of a chord are also the endpoints of an arc –Diameters perpendicular to chords bisect chords and intercepted arcs Homework: –pg ; 11-18; 30-33, 52