In Fig. 10.54, a circle touches all the four sides of a quadrilateral `A B C D` with `A B=6c m` , `B C=7c m` and `C D=4c m` . Find `A D` . (FIGURE)

A circle touches all the four sides of a quadrilateral A B C D . Prove that: A B+C D=B C+D A .

Find the area of a quadrilateral A B C D is which A B=3c m ,\ B C=4c m ,\ C D=4c m ,\ D A=5c m\ a n d\ A C=5c m

Find the area of the quadrilateral A B C D , in which A B=7c m ,B C=6c m ,C D=12 c m ,D A=15 cm and A C=9 cm

Find the area of the quadrilateral A B C D , in which A B=7c m ,B C=6c m ,C D=12 c m ,D A=15 c ma n dA C=9c m

Construct a quadrilateral A B C D in which A B=6c m ,\ B C=4c m ,\ C D=4c m ,\ \ /_B=95^0a n d\ /_C=90^0dot

Find the area of the quadrilateral A B C D , in which A B=7c m ,\ B C=6c m ,\ C D=12\ c m ,\ D A=15 c m\ a n d\ A C=9\ 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 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)

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

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 .