Monday, October 4, 2010

Problem: 525 Circles, Diameter, Tangent, Radius, Congruence, Measurement

Geometry Problem
Level: High School, SAT Prep, College geometry.
Click the figure below to see the complete problem 525 about Circles, Diameter, Tangent, Radius, Congruence, Measurement.

Problem 525: Circles, Diameter, Tangent, Radius, Congruence, Measurement

4 comments:

  1. Note that triangle AKJ similar to triangle AEO’ (case AA)
    So KJ/O’E=AJ/AO’ or r3/r2= (2r1-r3)/(d-r2)
    Develop above expression we get r3=2.r1.r2/d

    Similarly we also have triangle DNM similar to triangle DGO
    So r4/r1=(2.r2-r4)/(d-r1) and r4=2.r1.r2/d

    Peter Tran

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  2. ▲AGD ~ ▲CND => DG/DN = d/2r2
    ▲DOG ~ ▲DNM => DG/DN = r1/r4
    => r4 = (2r1r2)/d
    about r3 see ▲ADE, ▲AKB

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  3. (2*r1-r3)/r3=(d-r2)/r2 ---> 2*r1*r2=d*r3
    (2*r2-r4)/r4=(d-r1)/r1 ---> 2*r1*r2=d*r4 ---> r3=r4=2*r1*r2/d

    ReplyDelete
  4. yes you are right

    ReplyDelete