Proposed Problem

Click the figure below to see the complete problem 360 about Area of a triangle, Curvilinear triangles, Circles, Diameters.

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Complete Problem 360

Level: High School, SAT Prep, College geometry

## Tuesday, September 29, 2009

### Problem 360. Area of a triangle, Curvilinear triangles, Circles, Diameters.

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name blank area under AC : a, b

ReplyDeletename blank area above BC : c, f

name blank area on the left of AB : e, d

name area near A as α, near C as ß, near B as Φ

S3 + a + b = c + d + α + ß + S4

S2 + c + f = e + b + ß + Φ + S4

S1 + e + d = a + f + α + Φ + S4

S3+a+b+S2+c+f+S1+e+d=c+d+α+ß+S4+e+b+ß+Φ+S4+a+f+α+Φ+S4

S1 + S2 + S3 = 2α + 2ß + 2Φ + 2S4 + S4

S1 + S2 + S3 - S4 = 2 ( α + ß + Φ + S4 )

S1 + S2 + S3 - S4 = 2S

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To c.t.e.o

ReplyDeleteThe answer is ok.