In Fig, the line segment XY is parallel to side AC of `Delta ABC` and it divides the triangle into two parts of equal areas. Find the ratio `(AX)/(AB)`.

Show that a median of a triangle divides it into two triangles of equal areas.

If the sides of a Delta ABC are in AP and a is the smallest side, then cos A equals

Find the area of the triangle having all side equal to 8.

XY is a line parallel to side BC of triangle ABC. If BE II AC and CF II AB meet XY at E and F respectively,show that ar (ABE) = ar (ACF).

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. Prove it.

If a line is divided by three parallel lines into two segments of lengths in the ratio 1 : 3 another line will be divided by these parallel lines into two segments of lengths in the ratio .............. .