In any triangle ABC, show that AB*AB+AC*AC=2(AD*AD+BD*BD)where D is the midpoint of BC
Answer (1)
3rd Apr, 2019
Hello Arjun,
This question uses multiple properties of triangles.
The line joining one vertex of a triangle and the midpoint of the side opposite to the vertex is perpendicular to that side.
This means that AD is the height of the triangle
Now using Pythagoras theorem,
AD^2 = AB^2 + BD^2
Also AD^2 = AC^2 + DC^2
BD = DC
Adding the two equations you will get the required answer.
Hope this helps.
All the best!
This question uses multiple properties of triangles.
The line joining one vertex of a triangle and the midpoint of the side opposite to the vertex is perpendicular to that side.
This means that AD is the height of the triangle
Now using Pythagoras theorem,
AD^2 = AB^2 + BD^2
Also AD^2 = AC^2 + DC^2
BD = DC
Adding the two equations you will get the required answer.
Hope this helps.
All the best!
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