Monday, September 15, 2008

Elearn Geometry Problem 179

Rhombus, Square, Diagonal, Angle

See complete Problem 179 at:
www.gogeometry.com/problem/p179_rhombus_square_diagonal_angle.htm

Rhombus, Square, Diagonal, Angle. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

4 comments:

  1. DA=DC=DE, D is the circumcenter of CAE, mAEC=90°/2=45°

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  2. notice that AD = CD = DE so if we draw a circle with centre D and radius DE, say, then it will pass through A, C and E. but angle ADC is 90 degrees and it is also the central angle. so angle AEC will be half of angle ADC that is angle AEC = 45 degrees.
    Q.E.D.

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  3. D is the Centre of circle ACE and the result follows

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  4. See the drawing : Drawing

    CDEF Rombus =>DC=DE
    ABCD square =>DC=DA
    DA=DC=DE => A, C and E are on the circle with center D and radius AD
    With the theorem of inscribed angle, the central angle of a circle is twice any inscribed angle => ∠ ADC=2 ∠ CEA
    ∠ ACD=90° => ∠ CEA=45°

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