Wednesday, January 20, 2016

Geometry Problem 1181: Cyclic Quadrilateral and Tangential Quadrilateral, Diameter as a Diagonal, Incenter, Circumcenter

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 1181.

Online Math: Geometry Problem 1181: Cyclic Quadrilateral and Tangential Quadrilateral, Diameter as a Diagonal, Incenter, Circumcenter

Posted by Antonio Gutierrez at 6:35 AM
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3 comments:

  1. c.t.e.oJanuary 20, 2016 at 8:11 AM

    Ang B1=Ang B2 (BO bisector), => D1=D2 => AB=BC
    But BC-BF=3 => x=3

    ReplyDelete
  2. Sumith PeirisJanuary 20, 2016 at 9:08 AM

    BD is a diameter of circle ABCD and also bisects < ABC. Hence Tr. s ABD and BCD are congruent ASA.

    So AB = BC

    Hence x = BC - BF

    Now BC + 7 = BF + 10 since BCEF is a tangential quadrilateral

    So BC - BF = 3 and hence x = 3

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete
  3. Peter TranJanuary 20, 2016 at 10:20 AM

    Triangles BCD and BAD are right triangles
    ∠ (CBD)= ∠ (ABD) => Tri BCD congruence to BAD and BA=BC
    BCEF is a tangential quadrilateral so
    BF+CE=EF+BC => BC-BF=CE-EF= 10-7=3
    BA-BF=FA=3

    ReplyDelete

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