B Apply

20. Solar Eclipse Common tangents to two circles may be internal or external. If you draw a segment joining the centers of the circles, a common internal tangent will intersect the segment. A common external tangent will not. For this cross-sectional diagram of the sun, moon, and Earth during a solar eclipse, use the terms above to describe the types of tangents of each color.

    
    Image Long Description

    1. red
    2. blue
    3. green
    4. Which tangents show the extent on Earth's surface of total eclipse? Of partial eclipse?

21. Reasoning A nickel, a dime, and a quarter are touching as shown. Tangents are drawn from point A to both sides of each coin. What can you conclude about the four tangent segments? Explain.

    

22. Think About a Plan Leonardo da Vinci wrote, “When each of two squares touch the same circle at four points, one is double the other.” Explain why the statement is true.
    • How will drawing a sketch help?
    • Are both squares inside the circle?

23. Proof Prove Theorem 12-3.

    Given: B A ¯ b eh bar  and B C ¯ b c bar  are tangent to ⊙ O circle dot o  at A and C, respectively.

    Prove: B A ¯ ≅ B C ¯ b eh bar , approximately equal to , b c bar

    

24. Proof Given: B C ¯ b c bar  is tangent to ⊙ A circle dot eh  at D. D B ¯ ≅ D C d b bar . approximately equal to d c

    Prove: A B ¯ ≅ A C ¯ eh b bar , approximately equal to , eh c bar

    

25. Proof Given: ⊙ A circle dot eh  and ⊙ B circle dot b  with common tangents D F ¯ d f bar  and C E ¯ c e bar

    Prove: Δ G D C ∼ Δ G F E cap delta g d c tilde operator cap delta g f e

    

26. 1. A belt fits snugly around the two circular pulleys. C E ¯ c e bar  is an auxiliary line from E to B D ¯ . C E ¯ | | B A ¯ . b d bar , . . c e bar , vertical line vertical line . b eh bar , .  What type of quadrilateral is ABCE? Explain.
    2. What is the length of C E ¯ ? c e bar , question mark
    3. What is the distance between the centers of the pulleys to the nearest tenth?

    

27. B D ¯ b d bar  and C K ¯ c k bar  below are diameters of ⊙ A . B P ¯ circle dot eh . , b p bar  and Q P ¯ q p bar  are tangents to ⊙ A . circle dot eh .  What is m ∠ C D A ? m angle c d eh question mark

    

28. Constructions Draw a circle. Label the center T. Locate a point on the circle and label it R. Construct a tangent to ⊙ T circle dot t  at R.

29. Coordinate Geometry Graph the equation x 2 + y 2 = 9 . x squared , plus , y squared . equals 9 .  Then draw a segment from ( 0 , 5 ) open 0 comma 5 close  tangent to the circle. Find the length of the segment.

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