In ` A B C` , `P` divides the side `A B` such that `A P : P B=1:2` . `Q` is a point in `A C` such that `P Q B C` . Find the ratio of the areas of ` A P Q` and trapezium `B P Q C` .

In triangle A B C , a point P is taken on A B such that A P//B P=1//3 and point Q is taken on B C such that C Q//B Q=3//1 . If R is the point of intersection of the lines A Qa n dC P , using vector method, find the area of A B C if the area of B R C is 1 unit

In a triangle A B C , let P and Q be points on AB and AC respectively such that P Q || B C . Prove that the median A D bisects P Q .

A B C D is a parallelogram. P is a point on A D such that A P=1/3A D and Q is a point on B C such that C Q=1/3B P . Prove that A Q C P is a parallelogram.

In two similar triangles A B C and P Q R , if their corresponding altitudes A D and P S are in the ratio 4:9, find the ratio of the areas of triangle A B C and triangle P Q R .

In A B C , P Q is a line segment intersecting A B at P and A C at Q such that P Q B C and P Q divides A B C into two parts equal in area. Find (B P)/(A B) .

In Figure, P Q || B C and A P : P B=1:2 . Find (a r e a( A P Q))/(a r e a( A B C)) .

A B C D is a parallelogram. P is a point on A D such that A P=1/3\ A D\ a n d\ Q is a point on B C such that C Q=1/3B C . Prove that A Q C P is a parallelogram.

A B C D is a trapezium in which A B D C . P and Q are points on sides A D and B C such that P Q A B . If P D=18 , B Q=35 and Q C=15 , find A D .

In A B C , P and Q are points on sides A B and A C respectively such that P Q||B C . If A P=4c m ,\ \ P B=6c m and P Q=3c m , determine B C .

In fig.22, A B C is right angled at Adot\ Q\ \ a n d\ R are points on line B C and P is a point such that Q P||A C and R P||A B . Find /_Pdot