In Fig. 4.224, `D E C B` . Determine `A C` and `A 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. 4.103, C D and G H are respectively the medians of A B C and E F G . If A B C ~ F E G , prove that (FIGURE) A D C ~ F H G (ii) (C D)/(G H)=(A B)/(F E) (iii) C D B ~ G H E

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 Fig. 4.128, D E F G is a square and /_B A C=90o . Prove that A G F D B G (ii) A G F E F C (FIGURE) (iii) D B G E F C (iv) D E^2=B DxxE C

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. 4.95, 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. 4.101, A D and C E are two altitudes of A B C . Prove that A E F ~ C D F (ii) A B D ~ C B E (iii) A E F ~ A D B (iv) F D C ~ B E C (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 Figure, A D\ a n d\ B E are medians of A B C\ a n d\ B E||D F . Prove that C F=1/4A C

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