Saturday, December 21, 2013

Geometry Problem 948: Intersecting Circles, Secant, Cyclic Quadrilateral, Concyclic Points

Geometry Problem. Post your solution in the comments box below.
Level: Mathematics Education, High School, Honors Geometry, College.
Click the figure below to enlarge the problem 948.

Online Geometry Problem 948: Intersecting Circles, Secant, Cyclic Quadrilateral, Concyclic Points

Posted by Antonio Gutierrez at 3:35 PM
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4 comments:

  1. Jacob HA (EMK2000)December 21, 2013 at 5:38 PM

    Let S(B, k, θ) be a homothetic rotation transformation,
    centered at B, such that C₁→C₂, D₁→D₂.

    Then ∠D₁C₁B=∠D₂C₂B.
    Hence, BC₁FC₂ are concyclic.

    ReplyDelete
    Replies
    1. Peter TranOctober 17, 2016 at 10:28 PM

      To show that C2 and D2 are the image of C1 and D1 in the transformation S(B, k,θ) we need to show that ∠C1BC2=∠D1BD2 and BC2/BC1= BD2/BD1 .

      Peter Tran

      Delete
  2. ion raduDecember 24, 2013 at 7:13 AM

    ∠D₁C₁B=∠D₁AB deoareceBD₁C₁A concyclic,∠D₁AB.+∠D₂AB=180=>∠D₂C₂B=∠D₁C₁B si BC₁FC₂ concyclic.

    ReplyDelete
  3. Sumith PeirisFebruary 15, 2020 at 9:08 AM

    External angle at F = < FD1D2 + < FD2D1 = < ABC1 + < ABC2 = < C1BC2 and the result follows

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete

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