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CCSS Content Standards G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.C.1 Prove that all circles are similar. Mathematical Practices 4 Model with mathematics. 1 Make sense of problems and persevere in solving them.

Vocabulary circle center radius chord diameter concentric circles circumference pi (  ) inscribed circumscribed

Concept

Example 1 Identify Segments in a Circle A. Name the circle and identify a radius.

Example 1 Identify Segments in a Circle B. Identify a chord and a diameter of the circle.

Example 1 A. Name the circle and identify a radius. A. B. C. D.

Example 1 B. Which segment is not a chord? A. B. C. D.

Concept

Example 2 Find Radius and Diameter Answer: QV = 10.5 cm d= 2rDiameter Formula 21= 2rd = = rSimplify. If RT = 21 cm, what is the length of QV? RT is a diameter and QV is a radius.

Example 2 A.12 cm B.13 cm C.16 cm D.26 cm If QS = 26 cm, what is the length of RV?

Concept

Example 3 Find Measures in Intersecting Circles

Example 3 Find Measures in Intersecting Circles First, find ZY. WZ + ZY= WY 5 + ZY= 8 ZY= 3 Next, find XY. XZ + ZY= XY = XY 14= XY Since the diameter of is 16 units, WY = 8. Similarly, the diameter of is 22 units, so XZ = 11. WZ is part of radius XZ and part of radius WY.

Example 3 Find Measures in Intersecting Circles Answer: XY = 14 units

Example 3 A.3 in. B.5 in. C.7 in. D.9 in.

Concept

Example 4 Find Circumference CROP CIRCLES A series of crop circles was discovered in Alberta, Canada, on September 4, The largest of the three circles had a radius of 30 feet. Find its circumference. Since the radius is 30 feet, and d = 2r, the diameter = 2(30) or 60 feet. C=  dCircumference formula =  (60)Substitution = 60  Simplify. ≈ Use a calculator. Answer: The circumference of the crop circle is 60  feet or about feet.

Example 4 A feet B feet C feet D feet The Unisphere is a giant steel globe that sits in Flushing Meadows-Corona Park in Queens, New York. It has a diameter of 120 feet. Find its circumference.

Example 5 Find Diameter and Radius Find the diameter and the radius of a circle to the nearest hundredth if the circumference of the circle is 65.4 feet. Circumference Formula Substitution Use a calculator. Divide each side by.

Example 5 Find Diameter and Radius Answer:d ≈ ft; r ≈ ft Radius Formula Use a calculator.

Example 5 A.8.4 m B.5.35 m C.2.67 m D.16.8 m Find the radius of a circle to the nearest hundredth if its circumference is 16.8 meters.

Example 6 Read the Test Item You need to find the diameter of the circle and use it to calculate the circumference. Circumference of Circumscribed Polygon

Example 6 Solve the Test Item The radius of the circle is the same length as either leg of the triangle. The legs of the triangle have equal length. Call the length x. Pythagorean Theorem Substitution Divide each side by 2. Simplify. Take the square root of each side. Circumference of Circumscribed Polygon

Example 6 Answer: 6  units So the radius of the circle is 3. Circumference formula Substitution Circumference of Circumscribed Polygon

Example 6 A. B. C. D.

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