Precalculus

Points A, B, and C are on a circle such that angle ABC=45 degrees, AB=6, and AC=8. Find the area of the circle.

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asked by Katie
  1. AB = 6
    AC = 8
    all I need to know actually is AC = 8
    so
    circumference = 8 (360/45)
    = 64 = 2 pi r

    r = 32/pi

    pi r^2 = pi (1024/pi^2) = 326

    whatevers, miles, astronomical units, thumbs (I do physics not math)

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    posted by Damon
  2. Hmm 326 is not right... I'm also confused on "circumference = 8 (360/45) = 64 = 2 pi r" can you explain that a bit?

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    posted by Katie
  3. How about this way:

    Since AC supports a 45 degree angle at the circle, AC must support a 90 degree angle at the centre.
    let the radius be r
    r^2 + r^2 = 8^2
    2r^2 = 64
    r^2 = 32

    Area = pi r^2 = 32 pi or appr 100.53

    Notice just as Damon pointed out, we don't even need to know that AB = 6

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    posted by Reiny
  4. Oh I see! Yes, your answer is correct Reiny. Thanks!

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    posted by Katie

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