The det `Delta=|{:(d^2+r,de,df),(de,e^2+r,ef),(df,ef,f^2+r):}|` is divisible by

In the given figure,ABC is an equilateral triangle which is inscribed inside a circle and whose radius is r .Which of the following is the area of the triangle? (r+DE)^((1)/(2))(r-DE)^((3)/(2))(b)(r-DE)^((1)/(2))(r+DE)^(2)(c)(r-DE)^((1)/(2))(r+DE)^(2)(d)(r-DE)^((1)/(2))(r+DE)^((3)/(2))(d)

Suppose D (2,1), E (-5,7),F(-5,-5) are the mid points of the sides AB,BC and CA of the triangle ABC Find the slope of DF,DE and EF

In figure, seg EF is a diameter and seg DF is a tangent segment. The radius of the circle is r. Prove that, DExxGE=4r^(2) .

In Delta^(s)ABC and, AB"||"DE, AB=DE, BC=EF and BC"||"EF . Vertices A, B and C are joined to vertices D, E and F respectively (see figure). Show that (i) ABED is a parallelogram (ii) BCFE is a parallelogram (iii) AC = DF (iv) DeltaABC~=DeltaDEF

In the adjoining figure , seg EF is a diameter and seg DF is a tangent segment. The radius of the circle is r. Prove that, DEtimesGE=4r^2 .

In Delta^(s)ABC and, AB"||"DE, BC=EF and BC"||"EF . Vertices A, B and C are joined to vertices D, E and F respectively (see figure). Show that (i) ABED is a parallelogram (ii) BCFE is a parallelogram (iii) AC = DF (iv) DeltaABC~=DeltaDEF

In Delta^(s)ABC and, AB"||"DE, BC=EF and BC"||"EF . Vertices A, B and C are joined to vertices D, E and F respectively (see figure). Show that (i) ABED is a parallelogram (ii) BCFE is a parallelogram (iii) AC = DF (iv) DeltaABC~=DeltaDEF

If Delta DEF[-=sim?]Delta BCA, write the part (s) of Delta BCA that correspond to (i) /_E( ii) /_EF (iii)

The ratio of bar(DB) to bar(EF) is 4 to 9. If bar(DF)=2 , what is the distance from D to the midpont of bar(EF) ?