If G is an interior point of triangle ABC and GA+GB+GC=0, prove G is the centroid of the triangle ABC.
Shaghil Zahidi , 8 Years ago
Grade 12
Analytical Geometry> If G is an interior point of triangle ABC...
1 AnswersVikas TU
Last Activity: 7 Years ago
Dear Student,
Given: GA+GB+GC=0
=>-GA+GM+GC=0
=>2GD=AG=GB+GC
=>2GD=GB+GC
=>GD=(GB+GC)/2
so in triangle GBC, GD will be the median
similarly, we can prove for triangles GAB and GAC.
so G is the centroid of the triangle i.e. mid point of all medians. (proved)
Given: GA+GB+GC=0
=>-GA+GM+GC=0
=>2GD=AG=GB+GC
=>2GD=GB+GC
=>GD=(GB+GC)/2
so in triangle GBC, GD will be the median
similarly, we can prove for triangles GAB and GAC.
so G is the centroid of the triangle i.e. mid point of all medians. (proved)
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)
Thapar University)
Provide a better Answer & Earn Cool Goodies
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Other Related Questions on analytical geometry
- The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is
- The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is
analytical geometry
0 Answer Available
Last Activity: 2 Years ago
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
analytical geometry
0 Answer Available
Last Activity: 2 Years ago
show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0
show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0
analytical geometry
0 Answer Available
Last Activity: 2 Years ago
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.
analytical geometry
0 Answer Available
Last Activity: 3 Years ago
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
analytical geometry
0 Answer Available
Last Activity: 3 Years ago