Construct a quadrilateral `A B C D` in which BC `7. 5 c m ,\ A C=A D=6c m ,\ C D=5c m\ a n d\ B D=10 c mdot`

In Fig. 10.57, a circle is inscribed in a quadrilateral A B C D in which /_B=90o . If A D=23 c m , A B=29 c m and D S=5c m , find the radius r of the circle. (FIGURE)

In Figure, A B C D is a quadrilateral in which diagonal \ A C=84\ c m ; D L_|_A C ,\ B M_|_A C ,\ D L=16. 5\ c m and B M=12\ c m . Find the area of quadrilateral A B C Ddot

Calculate the area of the quadrilateral A B C D as shown in Fig.33, given that B D=42\ c m , A C=28\ c m , O D=12\ c m and A C_|_B D .

In Figure, diagonal A C of a quadrilateral A B C D bisects the angles A\ a n d\ C . Prove that A B=A D\ a n d\ C B=C D

A B C D is a cyclic quadrilateral in which: B C A D ,\ /_A D C=110^0\ a n d\ /_B A C=50^0dot Find /_D A C /_D B C=80^0\ a n d\ /_B A C=40^0dot Find /_B C D /_B C D=100^0a n d\ /_A B D=70^0 find /_A D B

In a parallelogram A B C D diagonals A C\ a n d\ B D intersect at O\ a n d\ A C=6. 8\ c m\ a n d\ B D=5. 6 c m . Find the measures of O C\ a n d\ O D .

Find the area of the following polygon, if A L=10 c m , A M=20 c m , A N=50 c m , A O=60 c m a n d A D=90 c mdot Figure

Which of the following pairs of triangles are congruent? If they are congruent, write out the pairs of equal angles. A B C : A B=3c m , B C=4c m , C A=2 c m D E F : D E=2 c m , E F=3 c m a n d F D=4 c m P Q R : P Q=17 c m , Q R=15 c m , P R=18 c m D E F : D E=18 c m , E F=17 c m , D F=15 c m .

In Figure, A B C D is a trapezium in which A B\ D C\ a n d\ D C=40\ c m\ a n d\ A B=60\ c mdot If X\ a n d\ Y are, respectively, the mid-points of A D\ a n d\ B C , prove that: a r\ (t r a pdotD C Y X)=9/(11)\ a r\ (t r a pdot(X Y B A)

In Figure, A B C D is a trapezium in which A B=7c m ,\ A D=B C=5c m ,\ D C=x\ c m , and distance between A B\ a n d\ D C is 4c m . Find the value of x and area of trapezium A B C D