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.

## Monday, October 4, 2010

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

Labels:
circle,
congruence,
diameter,
measurement,
radius,
tangent

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Note that triangle AKJ similar to triangle AEO’ (case AA)

ReplyDeleteSo 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

▲AGD ~ ▲CND => DG/DN = d/2r2

ReplyDelete▲DOG ~ ▲DNM => DG/DN = r1/r4

=> r4 = (2r1r2)/d

about r3 see ▲ADE, ▲AKB

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

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

yes you are right

ReplyDelete