Question Number 103179 by ajfour last updated on 13/Jul/20

Commented byajfour last updated on 13/Jul/20

If D and E are midpoints of   sides AC and AB  respectively,  of △ABC , find         ((blue area)/(area △ABC))    in terms of    sides a, b, c of the △.

Answered by ajfour last updated on 13/Jul/20

Let B is origin. C(0,a)  A(h,k)     h=csin B ,  k=bsin C  D(((a+h)/2), (k/2))   ;  E((h/2), (k/2)) ;  Eq. of CF:    y=−(h/k)(x−a)  Eq. of BG:  y=(((a−h)/k))x  Eq. of ⊥ on AB through E :     y−(k/2)=−((h/k))(x−(h/2))  Eq. of ⊥ on AC through D :    y−(k/2)=(((a−h)/k))(x−((a+h)/2))  ......