Wednesday, July 28, 2010

Problem 485: Square, Side, Circles, Tangent, Radius, Measurement

Geometry Problem
Click the figure below to see the complete problem 485 about Square, Side, Circles, Tangent, Radius, Measurement.

Problem 485: Square, Side, Circles, Tangent, Radius, Measurement
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Complete Problem 485

Level: High School, SAT Prep, College geometry

3 comments:

  1. Draw perpendiculars from centres of C2 & C3 (labelled as F & G) to AB & AD intersecting in E. EFG is a rt. angled triangle giving us FG^2= EF^2 + EG^2 or (a/2-x)^2+(a/4)^2=(a/4+x)^2 which can be solved to obtain x=a/6.
    Ajit

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  2. let be E center of C1,F center of C3
    u=mes(<CBE),v=mes(<ABF)
    in the corner B
    2u+2v=90;u+v=45
    tan(u)=1/2,tan(v)=2x/a=tan(45-u)=1/3
    x=a/6
    .-.

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  3. We can form a right triangle of by drawing parallels to AB thro O1 and O3

    This right triangle will have sides = to a/2-x, a/2+x and a/4

    Now use Pyhagoras and the result follows

    Sumith Peiris
    Moratuwa
    Sri Lanka

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