Question

BL and CM are medians of a traingle ABC right angled at A. Prove that ( BLsqua7+ CM square =) 5BC square ?
IV. Answer any one of the following questions
2 x 8 =10​

Answer 1

Answer:

BL is median

⇒ AL=CL=

2

1

AC →(1)

CM is median

⇒ AM = MB =

2

1

AB →(2)

InΔBAC

(BC)

2

=(AB)

2

+(AC)

2

InΔBAC

(BL)

2

=(AB)

2

+(

2

AC

)

2

4BL

2

=4AB

2

+(AC)

2

In ΔMAC,

(CM)

2

=(AM)

2

+(AC)

2

(CM)

2

=(

2

AB

)

2

+(AC)

2

4CM

2

=(AB)

2

+(AC)

2

NOW,(BC)

2

=(AB)

2

+(AC)

2

→(1)

4BC

2

=4(AB)

2

+(AC)

2

→(2)

4CM

2

=AB

2

+4AC

2

→(3)

ADD (2)&(3)

4BC

2

+4CM

2

=5AB

2

+5AC

2

4(BL

2

+CM

2

)=5BC

2