In `Delta ABC`, XY || AC and XY divides the triangle into two parts of equal area. Find the ratio of `(AX)/(XB)`.

There is an equilateral triangle with side 4 and a circle with the centre on one of the vertex of that triangle. The arc of that circle divides the triangle into two parts of equal area. How long is the radius of the circle?

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

(x) DEF is the pedal triangle of the equilateral Delta ABC. Find angle BED .

Prove that the area of a triangle is invariant under the translation of axes.

Ratio of the area of two similar triangle is 16:25. find the ratio of their sides.

The ratio of the sides of a triangle ABC is 1: sqrt3:2. Then the ratio A:B:C is-

Prove that two diagonals of a parallelogram divides it into four triangles of equal areas.

(ix) AD, BE and CF are the three medians of Delta ABC and intersect at G. The area of the Delta ABC is 36 Sq. cm. Find (a) the area of Delta AGB and (b) the area of the quadrilateral BDGF.

A triangle with equal sides has perimeter 9 cm. Then find the area of the triangle

Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio___