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$I$ is the incenter of $\triangle ABC$. We have $CE = 15$$AE = 6$, and $AB = 10$. Find $BC$.

[asy] size(150);pair B = (0,0);pair C = (4,0);pair A = (0.5,2);pair D = C*length(A-B)/(length(A-C)+length(A-B));pair EE = (C*length(B-A)+A*length(B-C))/(length(B-A)+length(B-C));pair F = (A*length(C-B)+B*length(C-A))/(length(C-B)+length(C-A));pair I = intersectionpoint(B--EE,C--F);draw(D--A--B--C--A^^B--EE^^C--F);label(

 

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$I$ is the incenter of $\triangle ABC$. We have $CE = 15$$AE = 6$, and $AB = 10$. Find $BF$.

[asy] size(150);pair B = (0,0);pair C = (4,0);pair A = (0.5,2);pair D = C*length(A-B)/(length(A-C)+length(A-B));pair EE = (C*length(B-A)+A*length(B-C))/(length(B-A)+length(B-C));pair F = (A*length(C-B)+B*length(C-A))/(length(C-B)+length(C-A));pair I = intersectionpoint(B--EE,C--F);draw(D--A--B--C--A^^B--EE^^C--F);label(

 Apr 23, 2022
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Do not post A O P S homework.

 Apr 23, 2022

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