In Fig. 4.34, `A ,\ B` and `C` are points on `O P ,\ O Q` and `O R` respectively such that `A B P Q` and `B C Q R` . Show that `A C P R` . (FIGURE)

In Fig. 4.238, S and T are points on the sides P Q and P R respectively of P Q R such that P T=2c m , T R=4c m and S T is parallel to Q R . Find the ratio of the areas of P S T and P Q R . (FIGURE)

In Fig. 4.90, if P O S ~ R O Q , prove that P S Q R . (FIGURE)

In Fig. 4.90, if P S Q R , prove that P O S ~ R O Q . (FIGURE)

A, B and C are the points (a, p), (b,q) and (c,r) respectively such that a, b and c are in AP and p,q and r in GP. If the points are collinear, then

In Figure, X\ a n d\ Y are the mid-points of A C\ a n d\ A B respectively, Q P\ B C\ a n d\ C Y Q\ a n d\ B X P are straight lines. Prove that a r\ (\ A B P)=\ a r\ (\ A C Q)

The pth, qth and rth terms of an A.P. are a, b and c respectively. Show that a(q – r) + b(r-p) + c(p – q) = 0

Prove that the figure formed by joining the mid-points of the pair of consecutive sides of a quadrilateral is a parallelogram. OR B A C D is a parallelogram in which P ,Q ,R and S are mid-points of the sides A B ,B C ,C D and D A respectively. A C is a diagonal. Show that : P Q|| A C and P Q=1/2A C S R || A C and S R=1/2A C P Q=S R (iv) P Q R S is a parallelogram.

p A N D q are any two points lying on the sides D C a n d A D respectively of a parallelogram A B C Ddot Show that a r( A P B)=a r ( B Q C)dot