How to find the circumcenter of triangle EFG with E(4, 4), F(4, 2), and G(8, 2)?

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Dane Brennan · Accepted Answer

Replace (4,4) in equation (1):(4−h)2+(4−k)2=r2  [2]Substitute (4,2) into equation [1]:(4−h)2+(2−k)2=r2  [3]For equation [1], substitute (4,2):(8−h)2+(2−k)2=r2  [4]Calculate equation [3] minus equation [2]:(4−h)2−(4−h)2+(4−k)2−(2−k)2=r2−r2Note the terms that are eliminated when you sum to 0:Undefined control sequence cancelUndefined control sequence cancelthe remaining terms&#039; squares should be expanded:(16−8k+k2)−(4−4k+k2)=0Combine like terms:12−4k=0k=3Subtract equation [3] from equation [4]:(8−h)2−(4−h)2+(2−k)2−(2−k)2=r2−r2Note the terms that are eliminated when you sum to 0:Undefined control sequence cancelUndefined control sequence cancelExpand the squares of the remaining terms:(64−16h+h2)−(16−8h+h2)=0Combine like terms:48−8h=0h=6Result: the circumcenter is (3,6)

How to find the circumcenter of triangle EFG with E(4, 4), F(4, 2), and G(8, 2)?

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