Example 13 : BL and CM are medians of atriangle ABC right angled at A.

1.	Example 13 : BL and CM are medians of atriangle ABC right angled at A. Prove that4 (BL' + CMP) = 5 BC2.
Answer» Since BL is the median AL=CL=1/2 AC .............(1) Similarly CM is the median AM = MB = 1/2 AB ........... (2) In triangle ABC BC^2 = AB^2 + AC^2 In triangle BAL BL^2 =AB^2 +AL^2 BL^2 =AB^2 +(AC/2)^2 On further little solving steps 4BL^2 =4AB^2 +AC^2 Then in triangle MAC CM^2 =AM^2 +AC^2 Doing same process here We get 4CM^2 =AB^2 +4AC^2 BC^2==AB^2+AC^2 4CM^2=AB^2+4AC^2adding the above equation4(BL^2+CM^2)=5BC^2

Example 13 : BL and CM are medians of atriangle ABC right angled at A. Prove that4 (BL' + CMP) = 5 BC2.

Answer»

Since BL is the median

AL=CL=1/2 AC .............(1)

Similarly CM is the median

AM = MB = 1/2 AB ........... (2)

In triangle ABC

BC^2 = AB^2 + AC^2

In triangle BAL

BL^2 =AB^2 +AL^2

BL^2 =AB^2 +(AC/2)^2

On further little solving steps

4BL^2 =4AB^2 +AC^2

Then in triangle MAC

CM^2 =AM^2 +AC^2

Doing same process here We get

4CM^2 =AB^2 +4AC^2

BC^2==AB^2+AC^2

4CM^2=AB^2+4AC^2adding the above equation4(BL^2+CM^2)=5BC^2