Monday, July 8, 2013

Problem 897: Intersecting Circles, Common External Tangent, Secant, Congruence.

Geometry Problem. GeoGebra, HTML5 Animation for iPad and Nexus.
Post your solution in the comments box below.

Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the dynamic geometry demonstration of problem 897.

Online Geometry Problem 897: Intersecting Circles, Common External Tangent, Secant, Congruence. GeoGebra, HTML5 Animation for iPad and more tablets

3 comments:

  1. Let Dx and Cy are the extension of CD and DC
    We have ∠(DAE)=∠ (EDx)= ∠(CDG)
    and ∠(FAC)= ∠(AFy)= ∠(DGC)
    But ∠(DAE)= ∠(FAC) => ∠(CDG)= ∠(DGC)
    So GDC is isosceles triangle and GC=GD

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  2. ∠DCA=∠CFA
    ∠CFA+∠CAF+∠ACF=180deg
    ∠GCD+∠DCA+∠ACF=180deg ---> ∠GCD=∠CAF
    similarly, ∠GDC=∠DAE
    ∠CAF=∠DAE, so ∠GCD=∠GDC ---> GC=GD

    ReplyDelete
  3. AngleGCD = CDA + CFA = DEA + DCA = GDC
    So Triangle GCD isosceles

    ReplyDelete