Question

In ABC PS a right triangle and sulght angled at B and MN are the mid point of AB and AC respectively. Then 4 (AN²+CM2)​

Answer 1

Answer:

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Answer 2

Answer:

5AC2

Step-by-step explanation:

Given, △ABC, M is mid point of AB and N is mid point of BC.

In △ABN,

AN2=AB2+BN2 (Pythagoras Theorem)

AN2=AB2+(2BC​)2   ....(1)

In △BMC,

MC2=BM2+BC2 (Pythagoras Theorem)

MC2=BC2+(2AB​)2  ....(2)

Add (1) and (2),

AN2+MC2=AB2+(2BC​)2+BC2+(2AB​)2

AN2+MC2=45​AB2+45​BC2

4(AN2+MC2)=5(AB2+BC2)

4(AN2+MC2)=5AC2 (Pythagoras Theorem in △ABC)