ABCD is a rectangle with AB=16 units and BC=12 units. F is a point on AB and E is a point on CD such that AFCE is a rhombus. Find the length of EF.

In the given rectangle ABCD, the sum of the lengths of two diagonals is equal to 52 cm and E is a point in AB, such that bar(OE) is perpendicular to bar(AB) . Find the lengths of the sides of the rectangle, if OE=5 cm.

ABCD is a trapezium in which AB||DC and let E be the mid point of AD. Let F be a point on BC such that EF||AB. Prove that F is mid point of BC.

ABCD is a trapezium in which AB || DC and E is the mid-point of AD. If F be a point on BC such that EF || DC, then prove that EF=1/2(AB+DC).

Let ABCD be a trapezium in which AB||DC and E be the mid-point of AD. If F be a point on BC such that EF||AB. Then EF, where F is the mid-point of BC, is equal to

ABCD is a rectangle where ratio of the length of AB and BC is 3 : 2. If P is the mid point of AB . Find sin angle CPB

ABCD is a square with sides of length 10 units. OCD is an isosceles triangle with base CD. OC cuts AB at point Q and OD cuts AB at point P. The area of trapezoid PQCD is 80 sq units. The length of altitude from O of the AOPQ (in units) is

ABCD is a trapezium in which AB||DC and let E be the mid point of AD. Let F be a point on BC such that EF||AB. Prove that EF=1/2(AB+DC)

In Figure,ABCD isa trapezium in which side AB is a parallel to side DC and E is the mid- point of side AD. If F is a point on the side BC such that the segment EF is paralle side DC. Prove that F is the mid point of BC and EF=(1)/(2)(AB+DC)

ABCD is a rectangle and P,R and S are the mid - points of the AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.