If `A B=7. 5 c m\ a n d\ C D=2. 5 c m ,` construct a segment whose length is equal to (i) `A B-C D` (ii) `2A B` (iii) `3C D` (iii)`A B+C D` (v) `2A B+3C D`

In an equilateral triangle A B C if A D_|_B C , then A D^2 = (a) C D^2 (b) 2C D^2 (c) 3C D^2 (d) 4C D^2

In Figure, ABD is a triangle right-angled at A and A C_|_B D . Show that (i) A B^2=B C.B D (ii) A C^2=B C.D C (iii) A D^2=B D.C D

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, if A D ,\ A E and B C are tangents to the circle at D ,\ E and F respectively. Then, (a) 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 triangle A B C ,/_A=30^0,H is the orthocenter and D is the midpoint of B C . Segment H D is produced to T such that H D=D T The length A T is equal to (a). 2B C (b). 3B C (c). 4/2B C (d). none of these

In Figure, A B C D is a trapezium in which A B || C D and A D=B C . Show that : (i) /_A=/_B (ii) /_C=/_D (iii) A B C~= B A D (iv) diagonal A C=d i agon a lB D

If A B C D E F such that D E=3c m , E F=2c m , D F=2. 5 c m , B C=4c m , then perimeter of A B C is (a) 18cm (b) 20cm (c) 12cm (d) 15cm

A B D is a right triangle right-angled at A and A C_|_B D . Show that A B^2=B CdotB D (ii) A C^2=B CdotD C (iii) A D^2=B DdotC D (iv) (A B^2)/(A C^2)=(B D)/(D C)

A B C D is a cyclic quadrilateral whose diagonals A C\ a n d\ B D intersect at P . If A B=D C , prove that: (i) P A B\ ~= P D C (ii) P A=P D\ a n d\ P C=P B (iii) A D || B C

In Fig. , A D=4c m , B D=3c m and C B=12 c m , find cottheta . (a) (12)/5 (b) 5/(12) (c) (13)/(12) (d) (12)/(13) (