In Fig. 4.88, ` A C B ~ A P Qdot` If `B C=8c m` , `P Q=4c m` , `B A=6. 5 c m` , `A P=2. 8 c m` , find `C A` and `A Q` . (FIGURE)

In Fig. 4.136, 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 . (FIGURE)

In Fig. 4.177, A C B A P Q . If B C=10 c m , P Q=5c m , B A=6. 5 c m and A P=2. 8 c m find C A and A Q . Also, find the area ( A C B): a r e a ( A P Q) . (FIGURE)

In Fig. 4.95, if /_A D E=/_B show that A D E ~ A B C . If A D=3. 8 c m , A E=3. 6 c m , B E=2. 1 c m and B C=4. 2 c m , find D E . (FIGURE)

In Fig. 4.178, D E B C (FIGURE) If D E=4c m , B C=6c m and Area ( A D E)=16 c m^2 , find the area of A B C . (ii) If D E=4c m , B C=8c m and Area ( A D E)=25 c m^2 , find the area of A B C . (iii) If D E : B C=3:5 . Calculate the ratio of the areas of A D E and the trapezium B C E D .

In Fig. 4.144, we have A B C D E F . If A B=6c m , C D=x\ c m , E F=10 c m , B D=4c m and D E=y\ c m , calculate the values of x and y . (FIGURE)

In a A B C ,\ \ D\ a n d\ E are points on the sides A B and A C respectively. For each of the following cases show that D E B C : A B=10. 8 c m ,\ \ B D=4. 5\ c m ,\ \ A C=4. 8 c m\ a n d\ A E=2. 8 c m (ii) A D=5. 7 c m ,\ \ B D=9. 5 c m ,\ \ A E=3. 3 c m\ a n d\ E C=5. 5 c m .

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 Fig. 4.230, 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 . (FIGURE)

In Fig. 4.57, A E is the bisector of the exterior /_C A D meeting B C produced in E . If A B=10 c m , A C=6c m and B C=12 c m , find C E . (FIGURE)

In Fig. 4.245, R S D B P Q . If C P=P D=11 c m and D R=R A=3c m . Then the values of x and y are respectively (FIGURE) 12 , 10 (b) 14 , 6 (c) 10 , 7 (d) 16 , 8