In Fig. 10.78, if `A D ,\ A E` and `B C` are tangents to the circle at `D ,\ E` and `F` respectively. Then, (FIGURE) `A D=A B+B C+C A` (b) `2A D=A B+B C+C A` (c) `3A D=A B+B C+C A` (d) `4A D=A B+B C+C A`

In Fig. 5.10, if A C=B D , then prove that A B=C D .

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

A B C D is a parallelogram and E\ a n d\ F are the centroids of triangles A B D\ a n d\ B C D respectively, then E F= (a) A E (b) B E (c) C E (d) D E

A,B,C and D have position vectors a,b,c and d, respectively, such that a-b=2(d-c). Then,

D ,\ E ,\ F are the mid-point of the sides B C ,\ C A\ a n d\ A B respectively of A B Cdot Then D E F is congruent to triangle. A B C (b) AEF (c) B F D ,\ C D E (d) A F E ,\ B F D ,\ C D E

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 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=4 , A E=8 , D B=x-4 , and E C=3x-19 , find x (ii) If A D=8 c m , A B=12 c m and A E=12 c m , find C E . (iii) If A D=4 c m , D B=4. 5 c m and A E=8 c m , find A C .

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 Figure, A B C D ,\ A B F E\ a n d\ C D E F are parallelograms. Prove that a r( A D E)=a r( B C F)

In Fig. 6.41, if A B|| D E , /_B A C=35^@ and /_C D E=53^@, find /_D C E .