Sunday, August 14, 2016

Geometry Problem 1245: Cyclic or Inscribed Quadrilateral, Circle, Arc, Midpoint, Measurement

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

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Geometry Problem 1245: Cyclic or Inscribed Quadrilateral, Circle, Arc, Midpoint, Measurement. Mobile Apps
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2 comments:

  1. Peter TranAugust 15, 2016 at 6:36 PM

    https://goo.gl/photos/Raksk92QKNNeK9wC6

    Observe that OE, OF , OG and OH perpendicular to AB, BC, CD and AD.
    Draw diameter FF’
    We have ∠ (EOF’)= ∠ (B) … ( both angles supplement to ∠ (EOF) )
    ∠ (HOG)= ∠ (B)…. ( both angles supplement to∠ (D))
    Triangles EOF’ congruent to HOG ( case SAS) => EF’= HG
    In right triangle FEF’ we have EF^2+EF’^2= EF^2+HG^2= 36+16= 52= 4. Radius^2
    Similarly FG^2+EH^2= 4. Radius^2= 25+x^2
    So x^2= 52-25=27 and x=3.sqrt(3)

    ReplyDelete
  2. Stan FulgerSeptember 1, 2016 at 1:19 PM

    Notice that GE_|_FH, thus EF^2+GH^2=FG^2+EH^2, wherefrom x^2=27.

    Best regards

    ReplyDelete

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