Saturday, August 13, 2016

Geometry Problem 1244: Circle, Radius, Perpendicular, Chord, Secant, Measurement. Mind Map

Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to view more details of problem 1244.


Geometry Problem 1244: Circle, Radius, Perpendicular, Chord, Secant, Measurement. Mind Map. Mobile Apps

3 comments:

  1. https://goo.gl/photos/FGTGW9iSkgxRKfx16

    Connect BF, BC and BD
    Note that C is the midpoint of arc BG
    Triangle BEC similar to FBC ( case AA)
    So CB^2=CE.CF
    Triangle DCB similar to BCA ( case AA)
    So CB^2=CD.CA
    And CE.CF=CD.CA or 4x 10= 3(x+3)
    So x= 31/3

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  2. Let AB cut the circle at G.

    In isoceles Tr. BCG,

    CG^2 - CE^2 = BE.GE = CE.EF = 24
    So CG^2 = 24 + 16 = 40

    Now < CGB = CBG = < GDA

    Hence < CGD = < DGB - < CGB = < DGB - < GDA = < GAD

    Hence CG^2 = CD.CA

    So 40 = 3(3+x) from whence x = 31/3

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete
  3. 2nd solution

    < CFD = < CGD = < EAD as before

    Hence AFED is cyclic and the result is easily calculated

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete