In a ` A B C` , `/_A B C=135o` . Prove that `A C^2=A B^2+B C^2+4\ a r( A B C)`

In A B C ,\ \ /_A=60o . Prove that B C^2=A B^2+A C^2-A B.A C .

In figure, ABC is a triangle in which /_A B C=90^@ and A D_|_B C . Prove that A C^2=A B^2+B C^2-2B C.B D .

In figure, ABC is triangle in which /_A B C > 90o and A D_|_C B produced. Prove that A C^2=A B^2+B C^2+2B C.B D .

In a quadrilateral A B C D , given that /_A+/_D=90o . Prove that A C^2+B D^2=A D^2+B C^2 .

In A B C , /_A is obtuse, P B_|_A C and Q C_|_A B . Prove that: A BxxA Q=A CxxA P (ii) B C^2=(A CxxC P+A BxxB Q)

Prove that a(b cos C- os B)=b^(2)-c^(2)

In a Delta ABC,/_A=60^(@), then prove that b+c=2a cos[(B-C)/(2)]

If A B C D is a parallelogram, then prove that a r\ (\ A B D)=\ a r\ (\ B C D)=\ a r\ (\ A B C)=\ a r\ (\ A C D)=1/2\ a r\ (|""|^(gm)A B C D)

A B C D IS A PARALLELOGRAM AND O is any point in its interior. Prove that: a r\ ( A O B)+\ a r\ ( C O D)=\ a r\ ( B O C)+\ a r( A O D) a r\ ( A O B)+a r\ (C O D)=1/2\ a r(^(gm)A B C D) Given: A parallelogram A B C D\ a n d\ O is a point in its interior. To Prove: a r\ (\ A O B)+\ a r( C O D)=a r\ ( B O C)+a r( A O D)

In a parallelogram A B C D , the bisector of /_A also bisects B C at Xdot Prove that A D=2A B