In ` A B C` Prove that `A B^2+A C^2=2(A O^2+B O^2)` , where `O` is the middle point of `B C`

In a quadrilateral A B C D , prove that A B^2+B C^2+C D^2+D A^2=A C^2+B D^2+4P Q^2, where P and Q are middle points of diagonals A C and B Ddot

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

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

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)

Prove that b^2c^2+c^2a^2+a^2b^2gtabc(a+b+c) , where a,b,c gt 0 .

Prove that b^2c^2+c^2a^2+a^2b^2gtabc(a+b+c) , where a,b,c gt 0 .

In o+ABC, prove that cos A+cos B+cos C<=(3)/(2)

In A B C ,A B=A C , and the bisectors of angles B and C intersect at point O . Prove that B O=C O and the ray A O is the bisector of angles B A Cdot

In A B C ,\ A B=A C , and the bisectors of angles B\ a n d\ C intersect at point Odot Prove that B O=C O\ and the ray A O is the bisector of angle B A C

If 2 vec A C = 3 vec C B , then prove that 2 vec O A =3 vec C B then prove that 2 vec O A + 3 vec O B =5 vec O C where O is the origin.