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

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)

If four sides of a quadrilateral A B C D are tangential to a circle, then A C+A D=B D+C D (b) A B+C D=B C+A D (c) A B+C D=A C+B C (d) A C+A D=B C+D B

If any quadrilateral ABCD,prove that sin(A+B)+sin(C+D)=0cos(A+B)=cos(C+D)

If A B C D is a quadrilateral in which A B C D and A D=B C , prove that /_A = /_B .

In Figure, diagonal A C of a quadrilateral A B C D bisects the angles A and C . Prove that A B=A D and C B=CD .

If A B C D is a cyclic quadrilateral in which A D || B C . Prove that /_B=/_C

A, B, C, D are the four angles, taken in order of a cyclic quadrilateral. Prove that, cot A + cot B + cot C + cot D = 0

If any quadrilateral ABCD, prove that "sin"(A+B)+sin(C+D)=0 "cos"(A+B)=cos(C+D)

If any quadrilateral ABCD, prove that "sin"(A+B)+sin(C+D)=0 "cos"(A+B)=cos(C+D)

If any quadrilateral ABCD, prove that "sin"(A+B)+sin(C+D)=0 "cos"(A+B)=cos(C+D)