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CPM Geometry Unit 10 Day 6 Cs50 Common Tangent

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This PPT explains a process to find the length of a common tangent between circles

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CPM Geometry Unit 10 Day 6 Cs50 Common Tangent

  1. 1. Unit 10 Day 6
  2. 2. Warm up <ul><li>Find the length of the belt around 2 tangent circles both with a radius 10. </li></ul>Length = 20 π + 40
  3. 3. CS50 a IN = 12” IL = 9” Find SA
  4. 4. CS50 a IN = 12” IL = 9” Find SA Hint #1 Draw IS and IA
  5. 5. CS50 a IN = 12” IL = 9” Find SA Hint #2 Draw IT Answer: SA =
  6. 6. CS50 b Find RE
  7. 7. CS50 b 8’ 8’ 14’ MA = 14 + 17 + 8 = 39 MB = 14 – 8 = 6 So since triangle MBA is a right triangle, 39 2 – 6 2 = BA 2 , therefore BA = 38.54’, which is the same as RE. 6’
  8. 8. How to solve common tangent problems. If the radius of the large circle is 14, the radius of the smaller circle is 10 and the circles are 10’ apart, find the length of the common tangent.
  9. 9. Step #1 – Draw the segment joining the centers of the circles If the radius of the large circle is 14, the radius of the smaller circle is 10 and the circles are 10’ apart, find the length of the common tangent.
  10. 10. Step #2 – Draw the radii to the points of contact. If the radius of the large circle is 14, the radius of the smaller circle is 10 and the circles are 10’ apart, find the length of the common tangent.
  11. 11. Step #3 – From the center of the smaller circle , draw a segment parallel to the tangent line. If the radius of the large circle is 14, the radius of the smaller circle is 10 and the circles are 10’ apart, find the length of the common tangent.
  12. 12. Step #3 – From the center of the smaller circle , draw a segment parallel to the tangent line. If the radius of the large circle is 14, the radius of the smaller circle is 10 and the circles are 10’ apart, find the length of the common tangent. 10 10 14 10 10 4
  13. 13. Step # 4 – Use the Pythagorean theorem and properties of rectangles to find the length of the common external tangent. If the radius of the large circle is 14, the radius of the smaller circle is 10 and the circles are 10’ apart, find the length of the common tangent. 10 10 14 10 10 4
  14. 14. Step # 4 – Use the Pythagorean theorem and properties of rectangles to find the length of the common external tangent. 10 10 14 10 10 4 34 2 – 4 2 = 1140, so √1140 = 33.76, therefore the length of the tangent is 33.76
  15. 15. Summary <ul><li>To find the length of a common tangent: </li></ul><ul><li>Draw a segment joining the centers of the circles </li></ul><ul><li>Draw the radii of both circles from the center to the points of contact </li></ul><ul><li>Draw a segment from the center of the smaller circle parallel to the tangent line </li></ul><ul><li>Use the Pythagorean theorem to find the length of the common tangent </li></ul>
  16. 16. Practice <ul><li>The centers of two circles with radii 4 and 11 are 25 units apart. Find the length of a common tangent. </li></ul>Length of common tangent = 24
  17. 17. Finish CS52 – CS58 for tomorrow!

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