Results 1 to 5 of 5

Math Help - two intersecting circles with a triangle

  1. #1
    Newbie
    Joined
    Dec 2007
    Posts
    23

    two intersecting circles with a triangle

    Two circles intersect and have a common chord 24 cm long. The centers of the circles are 21 cm apart. The radius of one circle is 13 cm. Find the radius of the other circle.

    I don't get it. Why won't the radii of the two circles be the same? If there's a way to figure it out, please don't do the math, just tell me how to do it....
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2009
    Posts
    591
    Quote Originally Posted by Itachi888Uchiha View Post
    Two circles intersect and have a common chord 24 cm long. The centers of the circles are 21 cm apart. The radius of one circle is 13 cm. Find the radius of the other circle.....
    Just draw a rough sketch: two intersecting circles.
    Draw the chord -- the line between the two intersections.
    Next drawn a line between the two radius points.
    It does not need to be accurate to scale. Freehand two circles & two lines.

    Then drawn a line from one of the circle intersection points to the center of one of the circles. Call that distance 13 -- the known radius.

    You now have a triangle:
    1. center of circle to an intersection point.
    2. intersection point to 1/2 the chord, or where the chord is intersected by the line connecting the two radii.
    3. from the mid point of the chord back to the center of the circle with known radius.

    Call the distance between the two circle centers, which is 21, as x, and 21-x.

    You now have three sides of a right triangle.
    x^2 + (24/2)^2 = 13^2. You can solve for x.
    Then use that info to work on the other (unknown) radius.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,386
    Thanks
    1476
    Awards
    1
    Quote Originally Posted by Itachi888Uchiha View Post
    Two circles intersect and have a common chord 24 cm long. The centers of the circles are 21 cm apart. The radius of one circle is 13 cm. Find the radius of the other circle.
    This is very easy problem. The solution involves the use of the Pythagorean Theorem.
    The line of centers bisects the common cord at right angles.
    The two radii are the hypotenuse of two right triangles.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Mar 2007
    Posts
    1,240

    Talking

    Quote Originally Posted by Itachi888Uchiha View Post
    I don't get it. Why won't the radii of the two circles be the same?
    Why would they be the same...?

    Quote Originally Posted by Itachi888Uchiha View Post
    Two circles intersect and have a common chord 24 cm long. The centers of the circles are 21 cm apart. The radius of one circle is 13 cm. Find the radius of the other circle.
    Draw two overlapping circles, with one larger than the other. (The particular scale doesn't really matter. The picture is just a place-holder.) In my drawing, the larger circle is on the left.

    Draw the line (the "chord") between the two intersection points. Draw the line, perpendicular to this, between the two centers. Note that this second line must split the chord in half.

    Draw one radius line from each center to one of the intersection points. In my drawing, I draw the radii up to the upper of the two points. Label one radius line as "13" and the other as "r". In my drawing, I labelled the left-hand circle's radius as "13".

    Note that you now have two right triangles. They share a height line of length 12 (being half of the chord's length), and they have hypotenuse values of 13 and r.

    The center-to-center line forms the bases of the two triangles. Label one base as "x" and the other as "y". In my picture, I labelled the left-hand triangle's base as "x".

    Apply the Pythagorean Theorem to the triangle with sides x, 12, and 13. Solve for x.

    Noting the x + y = 21, use the value for x to find the value for y.

    Using this value for y, along with the Pythagorean Theorem, find the value of r.

    If you get stuck, please reply showing how far you have gotten. Thank you!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Dec 2007
    Posts
    23
    Found the answer and it is 20........Thanks and sorry to all.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Non intersecting circles...
    Posted in the Geometry Forum
    Replies: 2
    Last Post: September 29th 2011, 12:23 PM
  2. Intersecting Circles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 7th 2011, 04:07 PM
  3. Intersecting Circles
    Posted in the Geometry Forum
    Replies: 2
    Last Post: March 26th 2011, 11:16 PM
  4. Two circles intersecting each other...
    Posted in the Geometry Forum
    Replies: 2
    Last Post: February 25th 2010, 10:32 AM
  5. intersecting circles
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: March 14th 2009, 12:22 AM

Search Tags


/mathhelpforum @mathhelpforum