The two medians `BE` and `CF` of `DeltaABC` intersect each other at the point `G` and if the line segment `FE` intersects the line segment `AG` at the point `O`, then prove that `AO=3OG`.

The medians BE and CF of the DeltaABC intersect each other at G and the line segment EF intersects AG at O. Prove that OA = 3.OG.

Two medians BE and CF of Delta ABC intersect at G. Prove that area of the quadrilateral AFGE=(1)/(3)Delta ABC.

Each of the two equal circles passes through the centre of the other and the two circles intersect each other at the points. A and B.If a straight ine through the point A intersects the two circles at points C and D prove that Delta BCD is an equilateral triangle.

In two circles , one circle passes through the centre O of the other circle and they intersect each other at the points A and B . A straight line passing through A intersect the circle passing through O at the point P and the circle with centre at O at the point R . BY joining P , B and R , B prove that PR= PB.

Two circles intersect each other at the points P and Q. Two straight lines through P and Q intersect on circle at the points A and C and the other circle at B and D . Prove that AC||BD.

The end points of a line segment are (2, 3), (4, 5). Find the slope of the line segment.

Two circle intersect each other at A and B and a straight line parallel to AB intersects the circles at C,D,E,F. Prove that CD = EF.

The diagonals AC and BD of the parallelogram ABCD intersect each other at O . Any straight line passing through O intesects the sides AB and CD at the points P and Q respectively . Prove that OP = OQ.

Two chords AC and BD of a circle intersect each other at the point O. If two tangents drawn at the points A and B intersect each other at the point P and two tangents drawn at the points C and D intersect at the point Q, prove that angle P+ angle Q =2 angle BOC. [GP-X]

Two two circle with their centre at P and Q intersect each other, at the point A and B . Through the point A , a straight line parallel to PQ intersects the two circles at the points C and D respectively . If PQ = 5 cm , then determine the lenght of CD .