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Geometry ProblemLevel: High School, SAT Prep, College geometry.Click the figure below to see the complete problem 525 about Circles, Diameter, Tangent, Radius, Congruence, Measurement.
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/dSimilarly we also have triangle DNM similar to triangle DGOSo r4/r1=(2.r2-r4)/(d-r1) and r4=2.r1.r2/dPeter Tran
▲AGD ~ ▲CND => DG/DN = d/2r2▲DOG ~ ▲DNM => DG/DN = r1/r4=> r4 = (2r1r2)/dabout r3 see ▲ADE, ▲AKB
(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
yes you are right