Saturday, January 31, 2015

Geometry Problem 1078: Square, Inscribed Circle, Tangent, Triangle, Area

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

Click the diagram below to enlarge it.

Online Math: Geometry Problem 1078: Square, Inscribed Circle, Tangent, Triangle, Area.

Posted by Antonio Gutierrez at 12:14 PM
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3 comments:

  1. Peter TranJanuary 31, 2015 at 5:45 PM

    http://s13.postimg.org/z1zzlirbr/pro_1078.png
    Draw lines per sketch
    Triangle T1T3F similar to triangle T3CH ( case AA)
    Ratio of similarity= FT3/CH=T1T3/T3C=2
    So FT3=2. CH
    S= ½. GT3.CH= (a+b).1/2. FT3
    So S=1/4.a.(a+b)

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  2. PravinFebruary 5, 2015 at 9:17 AM

    https://docs.google.com/file/d/0Bx5WrBkYmaBHRFdEVTh4a1ExcGc/edit

    Complete rectangle GCDE. Extend T3 OT1 to meet GE at H.
    G,F,T1,H are concyclic.
    So a(a + b) = T3F.T3G = T3T1. T3H = CD. GC = 2 CT3. GC = 4 S

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  3. Sumith PeirisMay 6, 2019 at 2:57 AM

    Drop a perpendicular CX from C to GT3. Let CX = h

    Tr.s T1FT3 & CXT3 are similar right triangles. Since CT3 = T1T3/2, h = a/2

    So S = h(a+b)/2 = a(a+b)/4

    Sumith Peiris
    Moratuwa
    Sri Lanka

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