In a square ABCD, A is joined to a point X on BC and D is joined to a point Y on AB. If AX = DY, prove that AX is perpendicular to DY.

The side BC of a triangle ABC is bisected at D;o is any point in AD,BO and CO produced meet AC and AB in E and F respectively and AD is produced to X so that D is the mid-point of OX. Prove that AO:AX=AF:AB and show that FE|BC.

square ABCD is a parallelogram point E is on side BC. Line DE intersects ray AB in point T . Prove that DExxBE=CExxTE .

In Figure,X and Y are two points on equal sides AB and AC of a o+ABC such that AX=AY. Prove that XC=YB

In Figure,X,Y are two points on equal sides AB and AC of a ABC such that AX=AY . Prove that XC=YB

In parallelogram ABCD, X and Y are mid-points of opposite sides AB and DC respectively. Prove that: (i)AX=YC (ii) AX is parallel to YC (iii)AXCY is parallelogram

Let ABCD be a square. An arc of a circle with A as centre and AB as radius is drawn inside the square joining the points B and D. Points P on AB, S on AD, Q and R on arc BD are taken such that PQRS is a square. Further suppose that PQ and RS are parallel toAC. Then, (area PQRS)/(area ABCD) is