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Math Help - This is probably really simple but they didn't word it right :(

  1. #1
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    Question This is probably really simple but they didn't word it right :(

    Okay I don't get this:



    The diagram above shows a flat surface containing a line and a circle with no points in common. Can you visualize moving the line and/ or circle so that they intersect at exactly one point? Two points? Three points? Explain each answer and illustrate each with an example when possible.

    And...

    3x/4=6/7

    And...



    The perimeter (the sum of the side lengths) of the triangle above is 52 units. Write and solve an equation based on the information in the diagram. Use your solution for x to find the measures of each side of the triangle. Be sure to confirm that your answer is correct.

    Please and thank you.
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  2. #2
    Senior Member DivideBy0's Avatar
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    I don't believe a line can intersect a circle at three points, but they sure can at two. When a line touches a circle at one point it is called a tangent. When a line touches at two points it is called a secant. See the attached diagram (thanks wikipedia). Don't confuse secant with chord. A chord is a line segment, while a secant is a line. So the secant keeps on going while a chord stops at the circumference.

    To solve for x in:

    \frac{3x}{4}=\frac{6}{7}

    Multiply both sides by 4,

    3x=\frac{24}{7}

    Then divide both sides by 3,

    x=\frac{8}{7}

    For the triangle, we know the perimeter is 52, so
    (7x-4)+(10x+3)+19=52
    17x+18=52
    17x=34
    x=2
    Attached Thumbnails Attached Thumbnails This is probably really simple but they didn't word it right :(-tangent.jpg  
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  3. #3
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    Red face

    Quote Originally Posted by DivideBy0 View Post
    I don't believe a line can intersect a circle at three points, but they sure can at two. When a line touches a circle at one point it is called a tangent. When a line touches at two points it is called a secant. See the attached diagram (thanks wikipedia). Don't confuse secant with chord. A chord is a line segment, while a secant is a line. So the secant keeps on going while a chord stops at the circumference.

    To solve for x in:

    \frac{3x}{4}=\frac{6}{7}

    Multiply both sides by 4,

    3x=\frac{24}{7}

    Then divide both sides by 3,

    x=\frac{8}{7}

    For the triangle, we know the perimeter is 52, so
    (7x-4)+(10x+3)+19=52
    17x+18=52
    17x=34
    x=2
    Thanks for the thorough answers genius! Love ya!
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