In Fig. 4.241, `D E B C` and `A D=1/2B D` . If `B C=4. 5 c m` , find `D E` . (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. 6.41, if A B|| D E , /_B A C=35^@ and /_C D E=53^@, find /_D C E .

In Fig. 71, if A B C D\ a n d\ C D E F ,\ find \ /_A C E

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. 4.220, D is the mid-point of side B C and A E_|_B C . If B C=a , A C=b , A B=c , E D=x , A D=p and A E=p and A E=h , prove that: (FIGURE) b^2=p^2+a x+(a^2)/4 (ii) c^2=p^2-a x+(a^2)/4 (iii) b^2+c^2=2 p^2+(a^2)/2

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 a A B C , D and E are points on the sides A B and A C respectively such that D E B C If A D=2 c m , A B=6 c m and A C=9 c m , find A E . (ii) If (A D)/(B D)=4/5 and E C=2. 5 c m , find A E . (iii) If A D=x , D B=x-2 , A E=x+2 and E C=x-1 , find the value of x .

In Fig. 7.21, A C\ =\ A E , A B\ =\ A D and /_B A D\ =/_E A C . Show that B C\ =\ D E .

In A B C , D and E are points on side A B and A C respectively such that D E B C\ and A D : D B=3:1 . If E A=3. 3 c m , then A C= 1. 1 c m (b) 4c m (c) 4. 4 c m (d) 5. 5 c m

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)