Sunday, October 7, 2018

Geometry Problem 1393: Monge's Circle Theorem, Three Circles and Three Pair of Common Tangents, Collinearity

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

Details: Click on the figure below.

Geometry Problem 1393: Monge's Circle Theorem, Three Circles and Three Pair of Common Tangents, Collinearity, Tutoring.

Posted by Antonio Gutierrez at 5:42 PM
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2 comments:

  1. Sumith PeirisOctober 7, 2018 at 8:06 PM

    AD / BD = rA / rB
    CE / AE = rC / rA
    BF / CF = rB / rC

    Multiplying the 3 equations RHS = 1
    Hence applying Menelaus the result follows

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete
  2. Peter TranOctober 7, 2018 at 11:38 PM

    Let radius of circles centered A, B and C are r1, r2 and r3
    Connect DAB, ECA and FCB
    We have DB/DA= r2/r1
    EA/EC= r1/r3
    FC/FB= r3/r2
    Multiply above expressions side by side we have DB/DA x EA/EC xFC/FA= 1
    So D, E, F are collinear per Menelaus theorem

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