In Fig. 10.20, the sides `A B ,\ B C` and `C A` of triangle `A B C` touch a circle with centre `O` and radius `r` at `P ,\ Q` and `R` respectively. (FIGURE) Prove that: 1) AB + CQ = AC + BQ

In the given figure the sides AB, BE and CA of triangle ABC touch a circle with centre O and radius r at P,Q and R respectively. Prove that : (i) AB+CQ=AC+BQ

In Fig. 10.97, the sides A B ,\ B C and C A of triangle A B C , touch a circle at P ,\ Q and R respectively. If P A=4c m , B P=3c m and A C=11 c m , then length of B C is (FIGURE) (a) 11cm (b) 10cm (c) 14cm (d) 15cm

In Fig.2, a quadrilateral ABCD is drawn to circumscribe a circle, with centre O, in such a way that the sides AB, BC, CD and DA touch the circle at the points P, Q, R and S respectively. Prove that AB + CD = BC + DA.

A circle is touching the side B C of A B C at P and touching A B and A C produced at Q and R respectively. Prove that A Q=1/2(P e r i m e t e r\ of\ A B C) .

A circle is touching the side BC of a triangle ABC at point P and touching AB and AC produced at Q and R respectively. Prove that AQ=(1)/(2)("perimeter of "triangle ABC).

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 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 .

In Fig. 7.48, sides AB and AC of DeltaA B C are extended to points P and Q respectively. Also, /_P B C\ \ A B .

In Fig. 10.101, P Q and P R are two tangents to a circle with centre O . If /_Q P R=46^o , then /_Q O R equals (a) 67^o (b) 134^o (c) 44^o (d) 46^o

In Figure, a quadrilateral A B C D is drawn to circumscribe a circle such that its sides A B ,\ B C ,\ C D and A D touch the circle at P ,\ Q ,\ R and S respectively. If A B=x\ c m , B C=7c m , C R=3c m and A S=5c m , then x= (a) 10 (b) 9 (c) 8 (d) 7