Consider 3 non collinear point A (9,3) ; B (7,-1) and C (1,-1). Let P ( a , b ) be the centre and ' R ' is the radius of the circle 'S' passing through A, B, C. Also H ( barx, bary) are the coordinates of the orthocentre of the triangle ABC whose area be denoted by triangle. If D , E and F are the middle points of BC , CA and AB respectively then the area of the triangle DEF is

Question

Consider 3 non collinear point A (9,3) ; B (7,-1) and C (1,-1). Let P ( a , b ) be the centre and ' R ' is the radius of the circle 'S' passing through A, B, C. Also H ( barx, bary) are the coordinates of the orthocentre of the triangle ABC whose area be denoted by triangle. If D , E and F are the middle points of BC , CA and AB respectively then the area of the triangle DEF is (A) 12 (B) 6 (C) 4 (D) 3

Tardigrade Admin · Accepted Answer

Area of Δ DEF =(1/4) operatornamearea( triangle ABC )=(1/4)|9 3 1 7 -1 1 1 -1 1|=3

12

6

4

3

Area of ΔDEF=41​area(△ABC)=41​∣∣​971​3−1−1​111​∣∣​=3

Area of $Δ D EF = \frac{1}{4} area (△ A BC) = \frac{1}{4} ∣ ∣ 971 3 - 1 - 1 111 ∣ ∣ = 3$