In Figure, each of `P A ,\ Q B ,\ R C` and `S D` is perpendicular to `l` . If `A B=6c m` , `B C=9c m` , `C D=12 c m` and `P S=36 c m` , then determine `P Q ,\ Q R` and `R S` .

In Fig. 4.91, Q A and P B are perpendiculars to A B . If A O=10 c m , B O=6c m and P B=9c m . Find A Q . (FIGURE)

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

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 P Q R , right-angled at Q ,\ P Q=3c m and P R=6c m . Determine /_P and /_R .

P and Q are points on sides A B and A C respectively of A B C . If A P=3c m , P B=6c m , A Q=5c m and Q C=10 c m , show that B C=3\ P Q .

In /_\P Q R , right-angled at Q ,\ P Q=3c m and P R=6c m . Determine /_P and /_R .

In Figure, /_\A C B ~ /_\A P Q . If B C=8c m , P Q=4c m , B A=6. 5 c m and A P=2. 8 c m , find C A and A Q .

In /_\ P Q R , M and N are points on sides P Q and P R respectively such that P M=15 c m and N R=8c m . If P Q=25 c m and P R=20 c m state whether M N || Q R .

In a A B C , P and Q are point on the sides A B and A C respectively, such that P Q// B C . If A P=2. 4 c m , A Q=2c m , Q C=3c m and B C=6c m , find A B and P Q .

In a triangle, P ,\ Q\ a n d\ R are the mid-points of sides B C ,\ C A\ a n d\ A B respectively. If A C=21\ c m ,\ B C=29 c m\ a n d\ A B=30 c m , find the perimeter of the quadrilateral A R P Q