True or False :
If four points A,B,C and D(in space) are such that |AB| = |AD| = |BC| = |CD| then they are the vertex of a rhombus.

(True/ False) If A, B, C, D are four points such that /_BAC = 30^@ and /_BDC = 60^@ , then D is the centre of the circle through A, B and C.

(True/ False) If A, B, C and D are four points such that /_BAC = 45^@ and /_BDC = 45^@ , then A, B, C, D are concyclic.

True or False statements : If and B are invertible matrices such that AB = BA, then (AB)^-1 = A^-1B^-1

In the fig. AC>AB and D is the point on AC such that AB=AD. Show that BC>CD

True or False statements : If A,B,C are three matrices such that both AB and AC are defined and are equal, then it implies that B and C are equal matrices.

In DeltaABC,if AC=8, BC=7 and D lies between A and B such that AD=2, BD=4, then the length CD equals

(True/ False) Two chords AB and CD of a circle are each at distances 4 cm from the centre. Then AB = CD.

In the DeltaABC,AB=a,AC=c and BC=b , then

If A,B,C and D are any four points in space prove that |quad vec (AB) xx vec (CD)+ vec (BC) xx vec (AD) + vec (CA) xx vec (BD)|=4(area of Delta ABC) .

In Fig. D is a point on side BC of triangleABC such that (BD)/(CD) = (AB)/(AC) . Prove that AD is the bisector of angleBAC .