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 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. 4.177, 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 Figure, /_A B C=90^o and B D_|_A C . If B D=8c m , A D=4c m , find C D .

In Figure, D E || B C in /_\ A B C such that B C=8c m , A B=6c m and D A=1. 5 c m . Find D E .

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 .

A B C is a triangle and P Q is a straight line meeting A B in P and A C in Q . If A P=1c m , P B=3c m , A Q=1. 5 c m , Q C=4. 5 cm , prove that area of Δ A P Q is one-sixteenth of the area of ΔA B C .

In a /_\ A B C , A D is the bisector of /_A , meeting side B C at D . (i) If B D=2. 5 c m ,\ \ A B=5c m and A C=4. 2 c m , find D C . (ii) If B D=2c m ,\ \ A B=5c m and D C=3c m , find A C . (iii) If A B=3. 5 c m , A C=4. 2 c m and D C=2. 8 c m , find B D .

In Fig. 4.42, A D is the bisector of /_B A C . If A B=10 c m . A C=14 c m and B C=6c m , find B D and D C . (FIGURE)

M ,\ N\ a n d\ P are the mid-points of A B ,\ A C\ a n d\ B C respectively. If M N=3c m ,\ N P=3. 5 c m\ a n d\ M P=2. 5 c m , calculate B C ,\ A B\ a n d\ A C

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 .