On a piece of graph paper, draw a circle that has a radius of 5 and center at ( 0, 0 ).

Transcription

1 10.1 Stat Thinking On a piece of gaph pape, daw a cicle that has a adius of 5 and cente at ( 0, 0 ). 1. aw the segment that connects the points ( 3, 4 ) and ( 4, 3) on the cicle. Is this segment a diamete? xplain you answe. 2. aw the segment that connects the point ( 3, 4) with the oigin. What is the name of this segment? xplain you answe. 3. Is it possible to daw a line that intesects the cicle only once? Is it possible to daw a line that intesects the cicle moe than twice? If so, add an example of these lines to you dawing Wam Up Find the value of umulative Review Wam Up etemine if the segment lengths fom a tiangle. If so, is the tiangle acute, obtuse, o ight? 1. 3, 7, and , 7, and , 6, and ,, and 5. 4, 4, and , 20, and eomety opyight ig Ideas Leaning, LL Resouces by hapte ll ights eseved.

2 Name ate 10.1 Pactice In xecises 1 5, use the diagam. 1. Name the cicle. 2. Name two adii. 3. Name two chods. F 4. Name a secant. 5. Name a tangent. In xecises 6 and 7, tell whethe is tangent to. xplain you easoning In xecises and 9, point is a point of tangency. Find the adius of In xecises 10 and 11, points and ae points of tangency. Find the value(s) of x x 4 2x 2 + 2x 2x + 1 7x onstuct with a 1-inch adius and a point outside of. Then constuct a line tangent to that passes though. 13. Two sidewalks ae tangent to a cicula pak centeed at P, as shown. P a. What is the length of sidewalk? xplain. b. What is the diamete of the pak? 20 ft 40 ft opyight ig Ideas Leaning, LL ll ights eseved. eomety Resouces by hapte 333

3 Name ate 10.1 Pactice In xecises 1 5, use the diagam. 1. Name two adii. 2. Name two chods. 3. Name a diamete. 4. Name a secant. 5. Name a tangent and a point of tangency. F In xecises 6 and 7, tell whethe is tangent to. xplain you easoning In xecises and 9, point is a point of tangency. Find the adius of In xecises 10 and 11, points and ae points of tangency. Find the value(s) of x x + 7 4x 2 1x 10 6x 3 x 2 + x When will two cicles have no common tangents? Justify you answe. 13. uing a basketball game, you want to pass the ball to eithe Playe o Playe. You estimate that Playe is about 15 feet fom you, as shown. a. ow fa away fom you is Playe? b. ow can you pove that Playe and Playe ae the same distance fom the basket? Playe 12 ft asket You 15 ft Playe 334 eomety opyight ig Ideas Leaning, LL Resouces by hapte ll ights eseved.

4 Name ate 10.1 nichment and xtension Lines and Segments That Intesect icles 1. In the figue, is tangent to cicle. Find the length of In the figue, O = 13 and is tangent to cicle O, whose diamete has a length of 1. Find. O In the figue, O = 10, m = 54, and and ae tangents to cicle O. Find. O Wite a paagaph poof fo the following. iven: icle and cicle IM and JL ae common tangents. I K J Pove: IM JL L M opyight ig Ideas Leaning, LL ll ights eseved. eomety Resouces by hapte 335

5 Name ate 10.1 Puzzle Time Why id The Scientists Stay t The Math Teache s ouse? Wite the lette of each answe in the box containing the execise numbe. omplete the sentence. 1. oplana cicles that intesect in one point ae called cicles. 2. chod is a segment whose ae on a cicle. 3. diamete is a(n) that contains the cente of the cicle. 4. (n) is a line that intesects a cicle in two points. 5. tangent is a line in the plane of a cicle that intesects the cicle in exactly one point, the point of. 6. oplana cicles that have a common cente ae called cicles. 7. line o segment that is tangent to two coplana cicles is called a(n) tangent.. In a plane, a line is tangent to a cicle if and only if the line is to a adius of the cicle at its endpoint on the cicle. 9. Tangent segments fom a common extenal point ae. Find the indicated answes using the diagam. 10. iven x = 2, y = 45, and z = 53, is tangent to cicle? Yes o no? 11. Find the adius y of cicle, given that x = 12 and z = y +. and ae points of tangency. Find the value of x using the diagam. 12. j = 3x + 1, k = 4x 5 j 13. j = 2 x 2x + 3, k = 4x 6 k 14. j = x + 5, k = 4x + 6 x y z nswes. yes. connected. lines I. chod. common. adius P. pependicula M. cotangent S. tangent L. ugency secant U. consistent R. 5 T. 0.5 N. endpoints. no W. conguent S. unique R. paallel. tangency V. concentic N. R. 2 I. 3 M. negative S eomety opyight ig Ideas Leaning, LL Resouces by hapte ll ights eseved.