In a triangle ABC with usual notations, the length of medians AD and CE are 18 and 27 respectively, CE is extended to intersect the circumcircle of triangle ABC at F . If AB = 24 and G is centroid of

Question

In a triangle ABC with usual notations, the length of medians AD and CE are 18 and 27 respectively, CE is extended to intersect the circumcircle of triangle ABC at F . If AB = 24 and G is centroid of the triangle, then which of the following is/are true?

TestHub · Accepted Answer

2 1 ​ 2 b 2 + 2 a 2 − 2 4 2 ​ = 27 \ 2 1 ​ 2 b 2 + 2.2 4 2 − a 2 ​ ​ = 18 a = 6 31 ​ , b = 3 70 ​ ​ ​ ​ D A GE = s ( s − a ) ( s − b ) ( s − c ) ​ = 4 27 ​ 55 ​

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