Monday, May 19, 2008

Elearn Geometry Problem 58



See complete Problem 58
Right Triangle, Pythagoras, Congruence. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

6 comments:

  1. Es simple:
    traze la altura DH
    el angulo BAC es el mismo que el angulo DHC
    como AC=DC entonces los triangulos rectangulos ABC y DHC son iguales entonces HC=c,BH=a-c,DH=a
    finalmente en el triangulo rectangulo BHD use teorema de pitagoras y se tiene
    (a-c)2+a2=x2

    ReplyDelete
  2. The solution is posted on http://www.osinfofrom.us/solution_problem58.html

    ReplyDelete
  3. Let angle DCB = z Then we've, z= angle BAC &
    cos(z) = cos(BAC) = c/b
    Thus, x^2= a^2 + b^2 - 2a*b*c/b since DC = b
    = a^2 + a^2 + c^2 -2a*c since b^2=a^2+c^2
    = a^2+(a-c)^2
    QED
    Ajit: ajitathle@gmail.com

    ReplyDelete
  4. This comment has been removed by a blog administrator.

    ReplyDelete
  5. Consider pt.F on BC such that B-F-C and FC=c ..(1)
    angle BAC=angle FCD...(2)
    AC=DC=b...given...(3)
    By (1),(2),(3) and SAS test of congruency,
    tri ABC is congruent to tri FCD
    hence,DF=a...(c.s.c.t) and
    angle DFC = angle DFB = 90
    Bf = a-c...(by(1))
    In tri DFB by pythagoras theorem,
    DE^2 + BE^2 = BD^2
    a^2 + (a-c)^2 = x^2

    ReplyDelete
  6. Extend AB to to E such thar AE equal a.Then AEC Tr congruent to BCD Tr.SAS.So CE equal x and the result folliws

    Sumith Peiris Sri Lanka

    ReplyDelete