100 200 300 400 500 Inscribed Angles Tangents & Angles Secants, Tangents, & Angles Segments In Circles Equations Of Circles.

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Presentation transcript:

Inscribed Angles Tangents & Angles Secants, Tangents, & Angles Segments In Circles Equations Of Circles

Inscribed Angles Answer: 90° AB is a diameter. Find m<BCA. A C B 35°

Inscribed Angles Answer: 50° Find m<CBD. C A B D 50°

Inscribed Angles P A D C B If the measure of arc AC = 72°, find m<ABC. Answer: 72/2 = 36° 72° 36°

Inscribed Angles Find the measure of arc BD. P A D C B 55° Answer: m<BCD = 35°, so arc BD = 70° 70° 35° 90°

Inscribed Angles Find the measure of arc ABD. P A D C B 36° 55° Answer: mAC = 72° and mCD = 110°, So mABD = 360 – ( ) = 178° 72° 110° 70° 108°

Tangents and Angles Answer: x 2 = 13 2, so x = 12 = BA Find BA. A B P 5 8 5

Tangents and Angles Answer: 4x + 18 = 7x, so x = 6 Find x. A B.P.P C 4x x

Tangents and Angles Answer: m<BPA = 48°, so mBC = 48° Find the measure of arc BC. D A B P C 42° 48°

Tangents and Angles Answer: 100° Find the measure of arc UV. R S T U V W X Y Z 40° 50° 40°

Tangents and Angles Answer: For UW: x 2 = 5 2, UW = 4 For XW: x 2 = 10 2, WX = 8, so UT = = 12 Find UT. R S T U V W X Y Z

Secants, Tangents, Angles Answer: m<EBC = 240/2 = 120° Find m<EBC.. D A C E B 240° 120°

Secants, Tangents, Angles Answer: m<3 = ( )/2 = 110° Find m<3. 60° D C A B C 160° 60° 80°

Secants, Tangents, Angles Answer: m<WXY = (105 – 55)/2 = 25° Find m<WXY. W X Y Z 105° 55° 200°

Secants, Tangents, Angles Answer: m<LJK = ( )/2 = 105º Find m<LJK 150º H I L K J N M 40º 110º 20º 40º

Secants, Tangents, Angles Answer: 4x + 6x + 11x x = 360, so x = 5. Then mKN = 110 º and mIM = 20º, so m<H = ( )/2 = 45 º Find m<H H I L K J N M (11x - 5)º (20x + 10)º (4x)º (6x)º 150º 110º 20º

Segments in Circles Answer: 6·3 = 9x, x = 2 Find x. D C A B C x

Segments in Circles Answer: 62 = 4(4 + x), x = 5 Find x. R S T U 6 x 4

Segments in Circles Answer: 4(4 + x) = 3(8), x = 2 P Find x. O N M L x

Segments in Circles Answer: x·x = 16 ·4, x = 8 Find x. C A B C 4 16 x D

Segments in Circles Answer: x(x + x) = 5(19.6), 2x 2 = 98, so x = 7 Find x. H G F E x x I

Equations of Circles Answer: (4, -5) What are the coordinates of the center of a circle with equation (x – 4) 2 + (y + 5) 2 = 16

Equations of Circles Answer: √34 = 5.8 What is the radius of a circle, as a decimal to the nearest tenth, with equation: (x – 4) 2 + (y + 5) 2 = 34.

Equations of Circles Answer: (x + 1) 2 + (y + 2) 2 = 9 Write the equation for circle K. K

Equations of Circles Answer: (x – 1) 2 + y 2 = 25 Find the equation of circle P. P

Equations of Circles Answer: The center of the circle is (1, 0) and the radius is 2. The easiest way to find the coordinates of a point on the circle would be to move 2 units above (1, 2), below (1, -2), left (-1, 0), or right (3, 0) of the center. Name the coordinates of a point on the circle with equation (x – 1) 2 + y 2 = 4