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Incircles of triangles proving a point it passes through

  1. Jan 31, 2013 #1
    1. The problem statement, all variables and given/known data
    I am given triangle ABC and a point X on the segment AB, one circle is inscribed inside triangle ACX and another inside BCX the two circles touch at point Y which lies on the line CX. show the inscribed circle of ABC touches AB at X


    2. Relevant equations
    I suppose you could use the fact the angle bisectors of a triangle is the incenter of the incircle and circumcircle of that triangle.


    3. The attempt at a solution
    So far i don't have a clue, but i have drawn the diagram. See attached.
    If anyone could just get me started i'd be so grateful
     

    Attached Files:

  2. jcsd
  3. Feb 2, 2013 #2

    tiny-tim

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    welcome to pf!

    hi mxl117! welcome to pf! :smile:

    ok, your difficulty here is that your diagram really isn't helping …

    the place you've put X, those circles should not be touching, so the whole diagram is misleading

    start again with a new diagram, and this time draw the incircle of ABC first (that's easy!),

    so that you know where X is, and your two small circles really do touch :wink:
     
  4. Feb 2, 2013 #3
    Thanks :)
    ahh sorry i thought i'd done everything the description asked.
    Do you have any hints about how to start proving it? because i'm stumped, sorry :(
     
  5. Feb 2, 2013 #4

    tiny-tim

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    hi mxl117! :smile:

    (i haven't solved it, but …)

    i'd certainly start by drawing in a third small circle that touches the first two small circles and the remaining pair of sides of the triangle …

    you now have a neat symmetric situation, with three small circles touching each other and the three sides :wink:
     
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