ABC is equilateral triangle and D,E are middle points of sides AB and AC then length of DE is

If the perpendicular distance from the centroid of an equilateral triangle to one of its sides is 'a' find the length of the radius of the inscribed circle

If the perpendicular distance from the centroid of an equilateral triangle to one of its sides is 'a' find the length of the radius of the circumscribed circle.

ABC is a triangle. D and E are two points on AB and AC respectively such that DE is parallel to BC and AD=1 cm , BD= 2cm . What is the ratio of the area of /_\ABC to the area /_\ADE .

ABC is an equilateral triangle of sides 2a.Find each of its altitudes.

If the perpendicular distance from the centroid of an equilateral triangle to one of its sides is 'a' find the length of its side

triangleABC and triangleDEF are two equilateral triangle such that D is the mid point of BC.The ratio of the areas of triangle ABC and BDE is

ABC is a triangle. D and E are two points on AB and AC such that DE and BC are parallel. If the area of DECB is m times the area of ADE then find (DB)/(AB) .

ABC and BDE are two equilateral triangles such that D is the mid-point of BC.Ratio of the areas of triangle ABC and BDE is a) 2:1 b) 1:2 c) 4:1 d) 1:4

ABCD is a parallelogram. E is the middle point of the side CD. BE intersects AC at the point X. prove that AX=2/3AC .

In triangle ABC,D and E are points on the sides AB and AC such that angleAED=angleC . Prove that triangleADE~triangleABC