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. 4.90, if P O S ~ R O Q , prove that P S 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)

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

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

In ΔABC a n d\ Δ P Q R ,\ A B=P Q ,\ B C=Q R\ a n d\ C B\ a n d\ R Q are extended to X\ a n d\ Y respectively and /_A B X=/_P Q Y . Prove that A B C~=\ P Q R .

In Figure, A P || B Q\ || C R . Prove that a r\ ( A Q C)=\ a r\ (P B R)