Equal chords AB and CD of a circle with centre O, cut at right angles at E. If L and M are the mid-points of AB and CD respectively, prove that OLEM is a square.

If in a triangle AB=a,AC=b and D,E are the mid-points of AB and AC respectively, then DE is equal to

Two equal chords AB and CD of a circle with centre O, intersect each other at E. Prove that AD = CB

ABC is an isosceles triangle in which AB = AC. If D and E are the mid-points of AB and respectively, prove that B,C,D and E are concyclic.

Two variable chords AB and BC of a circle x^(2)+y^(2)=a^(2) are such that AB=BC=a . M and N are the midpoints of AB and BC, respectively, such that the line joining MN intersects the circles at P and Q, where P is closer to AB and O is the center of the circle. The locus of the points of intersection of tangents at A and C is

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

Dand E are the mid-points of the sides AB and AC of DeltaABC and O is any point on side BC. O is joined to A. If P and Q are the mid-points of OB and OC respectively, then DEQP is

Two equal chords AB and CD of a cirlce when produced intersect at a point P. Prove that PB = PD.

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

In the fig. AE=DF where E and F are mid-points of AB and DC respectively.Using Euclid's axiom, prove that AB=DC

Two equal chords AB and CD of a circle C(O,r) when produced meet at a point E. Prove that: BE = DE