Question-132131

Question Number 132131 by Ar Brandon last updated on 11/Feb/21

Commented by Ar Brandon last updated on 11/Feb/21

Find the relation between the areas of

triangle ABC and triangle A^{'} B^{'} C^{'}

Commented by mr W last updated on 11/Feb/21

i f A, B, C a r e t h e m i d p o i n t s, t h e n

\frac{Δ_{A B C}}{Δ_{A^{'} B^{'} C^{'}}} = \frac{1}{7}

Commented by Ar Brandon last updated on 11/Feb/21

Sir, can you prove the theory ?

I tried, but got stucked .

Commented by mr W last updated on 11/Feb/21

Commented by mr W last updated on 11/Feb/21

e a c h o f t h e 7 s m a l l t r i a n g l e s h a s t h e

s a m e a r e a .

Commented by mr W last updated on 11/Feb/21

e x a m p l e :

A^{'} B = B A \Rightarrow Δ_{A^{'} B C} = Δ_{A B C}

B^{'} C = C B \Rightarrow Δ_{A^{'} B^{'} C} = Δ_{A^{'} B C} = Δ_{A B C}

Commented by Ar Brandon last updated on 11/Feb/21

OK Sir

Commented by Ar Brandon last updated on 11/Feb/21

Thanks