AB = CD. Prove that BE = and AE = Ce, where E is the point of intersection AD and BC.

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

In the fig ABCD is a parallelogram in which E and F are mid points of AB and CD respectively. Prove that the line segments CE and AF intersect diagonal BD

In two chords AB and CD intersect each AB and CD intersect each other at the point P. Prove that AP. PB = CP . DP

ABCD is a trapezium in which AB || DC . M and N are the mid-points of AD and BC respectively. If AB = 12 cm, and MN = 14 cm, find CD.

ABCD is a trapezium with AB II DC, E and F are paints on non-parallel sides AD and BC respectively such that EF is parallel to AB Show that (AE)/(ED)=(BF)/(FC) .

In triangleABC , D is the mid point of the side AB and E is centroid of triangleCDA . If OE*CD=0 , where O is the circumcentre of triangleABC , using vectors prove that AB=AC.

ABCD is a parallelogram E is the mid point of AB and CE bisects angleBCD . Prove that: AE=AD?

In two chords AB and CD intersect each AB and CD intersect each other at the point P. Prove that Delta APC ~ Delta DPB

ABC is a right triangle such that AB=AC and bisector of angle C intersects the side AB at D. prove that AC+AD=BC.

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