Statement 1 : Points `A(1,0),B(2,3),C(5,3),a n dD(6,0)` are concyclic. Statement 2 : Points `A , B , C ,a n dD` form an isosceles trapezium or `A Ba n dC D` meet at `Edot` Then `E AdotE B=E CdotE Ddot`

The distinct points A(0,0),B(0,1),C(1,0), and D(2a,3a) are concyclic than

Prove that the points A(4, 0), B(6, 1), C(4, 3) and D(3, 2) are concyclic.

Prove that A(4,3),B(6,4)a n dC(5,6)a n dD(3,5) are the angular points of a square.

A B C D is a cyclic quadrilateral. A Ba n dD C are produced to meet in Edot Prove that E B C-E D Adot

Statement 1:Let A( vec a),B( vec b)a n dC( vec c) be three points such that vec a=2 hat i+ hat k , vec b=3 hat i- hat j+3 hat ka n d vec c=- hat i+7 hat j-5 hat kdot Then O A B C is a tetrahedron. Statement 2: Let A( vec a),B( vec b)a n dC( vec c) be three points such that vectors vec a , vec ba n d vec c are non-coplanar. Then O A B C is a tetrahedron where O is the origin.

Statement 1: Distance of point D( 1,0,-1) from the plane of points A( 1,-2,0) , B ( 3, 1,2) and C( -1,1,-1) is 8/sqrt229 Statement 2: volume of tetrahedron formed by the points A,B, C and D is sqrt229/ 2

Statement 1: Let vec a , vec b , vec ca n d vec d be the position vectors of four points A ,B ,Ca n dD and 3 vec a-2 vec b+5 vec c-6 vec d=0. Then points A ,B ,C ,a n dD are coplanar. Statement 2: Three non-zero, linearly dependent coinitial vector ( vec P Q , vec P Ra n d vec P S) are coplanar. Then vec P Q=lambda vec P R+mu vec P S ,w h e r elambdaa n dmu are scalars.

A parallelepiped S has base points A ,B ,Ca n dD and upper face points A^(prime),B^(prime),C^(prime),a n dD ' . The parallelepiped is compressed by upper face A ' B ' C ' D ' to form a new parallepiped T having upper face points A",B",C"a n dD" . The volume of parallelepiped T is 90 percent of the volume of parallelepiped Sdot Prove that the locus of A" is a plane.

Any point D is taken in the base B C of a triangle A B C\ a n d\ A D is produced to E , making D E equal to A Ddot Show that a r\ ( B C E)=a r( A B C)

A B C is a triangle. D is a point on A B such that D=1/4A B\ a n d\ E is a point on A C such that A E=1/4A Cdot Prove that D E=1/4B C