Diagonals AC and BD of quadrilateral ABCD intersect each other at P. Show that ar `(APB) xx ar (CPD)` = ar `(APD)xx ar(BPC)`.

Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) = ar (BOC). Prove that ABCD is a trapezium.

Diagonals AC and BD of quadrilateral ABCD interset at O such that OB = OD , If AB = Cd, then show that : ar(DCB) = ar(ACB)

The diagonal AC and BD of a rectangle ABCD intersect each other at P. if angleABD=50^@ and angleDPC =

The diagonals of a quadrilateral ABCD intersect each other at the point o Such that (AO)/(BO)=(CO)/(DO) , show that ABCD is trapezium.

If the medians of a triangleABC intersect at G, show that ar(AGB) = ar(AGC) = ar(BGC) = 1/3 ar(ABC)

If the medians of a triangleABC intersect at G, show that ar(AGB) = ar(AGC) = ar(BGC) = 1/3 ar(ABC)

If bisectors of /_A and /_B of a quadrilateral ABCD intersect each other at P, of /_B and /_C at Q, of /_C and /_D at R and of /_D and /_A at S, then PQRS is a

Diagonals AC and BD of a parallelogram ABCD intersect each other at O. if OA=3 cm and OD=2 cm, determine the length of AC and BD.

In Fig. 9.27, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that:- (i) ar (ACB) = ar (ACF) (ii) ar (AEDF) = ar (ABCDE)