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mckenzieandjesus

  • one year ago

Point P is the center of two concentric circles. PQ = 10.5 and PS = 20.9. RS is tangent to the smaller circle and a chord of the larger circle. What is length of RS to the nearest tenth? 36.1 41.4 31.4 41.8

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  1. mckenzieandjesus
    • one year ago
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  2. mckenzieandjesus
    • one year ago
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    I think it is C

  3. campbell_st
    • one year ago
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    well the tangent RS and the radius PQ are perpendicular to each other, so you need pythagoras \[PS^2 = QS^2 + PQ^2\] then you need to know the perpendicular from the centre to the chord bisects the chord so RQ = QS or RS = 2QS hope it helps

  4. campbell_st
    • one year ago
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    and I don't think its C

  5. mckenzieandjesus
    • one year ago
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    i got 547 30/50

  6. mckenzieandjesus
    • one year ago
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    547 30/50^2 is 299274.6436

  7. campbell_st
    • one year ago
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    well using pythagoras' theorem you need to find QS manipulating the equation \[QS^2 = PS^2 - PQ^2\] so \[QS^2 = 20.9^2 - 10.5^2\] so start by finding QS then double it to get RS

  8. mckenzieandjesus
    • one year ago
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    20.9^2-10.5^2= 326 14/25

  9. mckenzieandjesus
    • one year ago
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    326 14/25^2 is 106641.4336

  10. phi
    • one year ago
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    you don't want to square 326.56 you want to (or should want to) take the *square root*

  11. mckenzieandjesus
    • one year ago
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    so 18.0709712

  12. phi
    • one year ago
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    and as campbell posted (see up above), that is 1/2 of the length you want.

  13. mckenzieandjesus
    • one year ago
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    so do i add 1/2?

  14. mckenzieandjesus
    • one year ago
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    or do 18.0709712^2?

  15. phi
    • one year ago
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    multiply by 2

  16. campbell_st
    • one year ago
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    so that is QS now the perpendicular line from the centre, PQ, bisects RS. so RS = 2 x QS so you know QS, just double it... to find RS

  17. phi
    • one year ago
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    or add to itself

  18. mckenzieandjesus
    • one year ago
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    36.1419424

  19. phi
    • one year ago
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    now round to the nearest tenth

  20. mckenzieandjesus
    • one year ago
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    so 36.1?

  21. phi
    • one year ago
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    yes

  22. campbell_st
    • one year ago
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    that's correct... now round it to 1 decimal place

  23. mckenzieandjesus
    • one year ago
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    36.1?

  24. campbell_st
    • one year ago
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    correct

  25. mckenzieandjesus
    • one year ago
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    what message?

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