In AABC, ZB=90°. M and N are the midpoints of AB and BC
respectively, then 4(AN? + CM2) =
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Answer:
hey guys this is your answer for the above question
Step-by-step explanation:
Given, △ABC, M is mid point of AB and N is mid point of BC.
In △ABN,
AN
2
=AB
2
+BN
2
(Pythagoras Theorem)
AN
2
=AB
2
+(
2
BC
)
2
....(1)
In △BMC,
MC
2
=BM
2
+BC
2
(Pythagoras Theorem)
MC
2
=BC
2
+(
2
AB
)
2
....(2)
Add (1) and (2),
AM
2
+MC
2
=AB
2
+(
2
BC
)
2
+BC
2
+(
2
AB
)
2
AM
2
+MC
2
=
4
5
AB
2
+
4
5
BC
2
4(AM
2
+MC
2
)=5(AB
2
+BC
2
)
4(AM
2
+MC
2
)=5AC
2
(Pythagoras Theorem in △ABC)
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