DEF is the triangle formed by joining the points of contact of the incircle with the sides of the triangle ABC : prove that
its area is `(2triangle^2)/(abcs), i.e. (1)/(2) (r )/(R )triangle`.

DEF is the triangle formed by joining the points of contact of the incircle with the sides of the triangle ABC : prove that its sides are 2r cos (A)/(2), 2r cos (B)/(2)," and " 2r cos (C )/(2) .

DEF is the triangle formed by joining the points of contact of the incircle with the sides of the triangle ABC : prove that its angles are (pi)/(2) - (A)/(2), (pi)/(2) - (B)/(2)" and " (pi)/(2) - (C )/(2) .

Find the area of the triangle formed by joining the mid -points of the sides of the triangle ABC ,whose vertices are A(0,-1),B(2,1)andC(0,3).

If triangle ABC cong triangle DEF then

Find the area of a triangle ABC if the coordinates of the middle points of the sides of the triangle are (-1, -2), (6, 1) and (3, 5)

A triangle DEF is formed by joining mid points of sides of triangle ABC. Again mid points of sides of triangle DEF are joined together to form a new triangle PQR. If sides of triangle ABC are respectively 4, 5 and 6 cm then what is the distance between centroid of DeltaPQR and DeltaDEF .