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Math Help - Trapezoids midline question

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    Trapezoids midline question

    Does the midline of a isosceles trapezoid run through the incenter of the trapzezoid?
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    Re: Trapezoids midline question

    Quote Originally Posted by Aquameatwad View Post
    Does the midline of a isosceles trapezoid run through the incenter of the trapzezoid?
    how is incenter of a trapezoid defined?
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    Re: Trapezoids midline question

    The intersection of the angle bisectors of the trapezoid?
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    Re: Trapezoids midline question

    Quote Originally Posted by Aquameatwad View Post
    The intersection of the angle bisectors of the trapezoid?
    all the four angle bisectors may not intersect at the same point. even any three of the angle bisectors may not intersect at the same point. this way we may have 4 different incentres. considering this the question is ill-posed.
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    Re: Trapezoids midline question

    The reason i ask is because im trying to figure out the area of a trapezoid with 2 inscribed circles with radius=1 and another with radius=3. I'm a bit lost. Heres a picture, its not drawn to scale
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    Re: Trapezoids midline question

    Quote Originally Posted by Aquameatwad View Post
    The reason i ask is because im trying to figure out the area of a trapezoid with 2 inscribed circles with radius=1 and another with radius=3. I'm a bit lost. Heres a picture, its not drawn to scale
    assuming that the trapezoid is isoceles, you need to figure out the base angles of this trapezoid. this can be done using trigonometry but its difficult to post it here. Try doing this:
    join the centres of the two circles. note that the sides of this trapezoid are nothing but the direct common tangents of these two circles. you just have to find the angle of inclination of the DCT to the line joining the centres. its easy. then finding the base angles is straightforward.
    the distance between the parallel sides is 3+3+1+1=8.

    once you get the above said thing you can find the lengths of each of the parallel sides. can you finish?
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    Re: Trapezoids midline question

    i see what you mean that the height is of the trapezoid 8. But im still lost.
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    Senior Member abhishekkgp's Avatar
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    Re: Trapezoids midline question

    Quote Originally Posted by Aquameatwad View Post
    i see what you mean that the height is of the trapezoid 8. But im still lost.
    i presume that you did not understand the DCT part.
    try solving a separate question:
    Two circles, one of radius 3 and the other of radius 1 are touching externally at a point. Draw the direct common tangents of these circles. what is the angle between these two direct common tangents??
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    Re: Trapezoids midline question

    I'm still a bit confused. But i will try my best to understand
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    Re: Trapezoids midline question

    Hello aquameatwad,
    First find the length of a common tangent.Two sides of a defining right triangle are available by drawing a few construction lines.Try this and see if you can go forward. Similar triangles are involved. If stuck repost.
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    Re: Trapezoids midline question

    Still stuck bj. We have not really gone into tangent lines in depth in class, so i dont know how to use them to find lengths.
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    Re: Trapezoids midline question

    Hi aquameatwad,
    Look at post 6.Extend the slant lines to meet at A. Bottom corners Band C.From centers draw perpendiculars to one common tangent meeting at the points of tangency.Draw a perpendicular from center r=1 to the radius 3.Formed is a rectangle height 1 and length common tangent and a rt triangle hyp 4 side 2.This gives you a ct of 2rad3.It also supplies info on triangle ABC.Carry on from there



    bjh
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