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)) ......