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Math Help - Find a Radius

  1. #1
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    Find a Radius

    A circle has a chord, AB, of 20cm. Point C is on AB, 8cm from A (and 12cm from B. I'm not entirely hopeless!) Point D is on the circle, 6cm from point C, and CD is perpendicular to AB.

    -What is the radius of the circle?
    -How far is point C from the center?
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  2. #2
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    Quote Originally Posted by English Major View Post
    A circle has a chord, AB, of 20cm. Point C is on AB, 8cm from A (and 12cm from B. I'm not entirely hopeless!) Point D is on the circle, 6cm from point C, and CD is perpendicular to AB.

    -What is the radius of the circle?
    -How far is point C from the center?
    1. Draw a sketch (see attachment)

    2. F is the midpoint of AB. Then the center of the circle is placed on a line through F perpendicular to AB.

    3. The distance of the center of the circle to AB is called x.

    4. You get 2 right triangles with the radius as hypotenuse. (Note that CF = 2) Use Pythagorean theorem:

    (6+x)^2 + 2^2 = r^2 ........ [1]

    x^2 + 10^2 = r^2 ........ [2]

    5. Solve for x:

    (6+x)^2 + 2^2 = x^2 + 10^2 ........ I've got x = 5

    6. Thus r = 5\cdot \sqrt{5}

    7. I'll leave the rest for you.
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