12:of G is the centroid of AABC, then
AG² +BG ²+CG²/
AB²+ BC ²+CA²
Answers
Answered by
54
Answer:
Answer:
1/3
Step-by-step explanation:
Consider AG² + BG²+ CG²
If AD, BE and CF are the medians , we know that centroid divides the median in the ratio 2:1, thus
= (2/3*AD)² + (2/3*BE)² + (2/3*CF)²,
= 4/9[ AD² + BE² + CF²]
Now we know length of median formula
Similarly BE² = AD² = 1/4*[2*(AB²+BC²)-AC²] , and
CF² = 1/4*[2*(BC²+AC²)-AB²]
Therefore,
AG² + BG²+ CG² = 4/9*1/4*3*(AB²+BC²+AC²)
=1/3*(AB²+BC²+AC²)
Thus, AG² + BG²+ CG²/AB²+BC²+AC² = 1/3.
Similar questions
Science,
4 months ago
Social Sciences,
4 months ago
Economy,
4 months ago
Social Sciences,
9 months ago
Math,
9 months ago