Geometry Problem. Post your solution in the comment box below.

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

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## Saturday, January 31, 2015

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

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http://s13.postimg.org/z1zzlirbr/pro_1078.png

ReplyDeleteDraw 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)

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

ReplyDeleteComplete 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

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

ReplyDeleteTr.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