Question

In right angled triangle BAC, angle BAC=90°, Segments AD,BE and CE are medians.
Peove that :
$2(ad { }^{2} + be ^{2} + cf {}^{2} ) = 3bc {}^{2}$
please​

Answer 1

Answer:

Which class question is this

Answer 2

Answer:

Draw right angle triangle ABC,

draw medians.  AD, BE, CF.  Now Join DF.

Since D and F are midpoints of sides AB and BC,  DF will be parallel to AC and is equal to 1/2 AC.

ADF, ABE, AFC are all  right angle triangles.

LHS = 2 (AD² +  BE² +  CF² )

       = 2 [ (AF² + DF²) + (AB² + AE²) + (AF² + AC²) ]

    =  2 [ (AB²/4 + AC²/4)  + (AB² + AC²) + (AC²/4 + AB²/4) ]

      = 2 [ BC² /2 +  BC² ]

      = 3 ( BC² ]

Step-by-step explanation: