If ABCD is a square then show that the points, A,B, C and D are concyclic.

In Figure, A B C is a triangle in which A B=A Cdot Point D and E are points on the sides AB and AC respectively such that A D=A Edot Show that the points B , C , E and D are concyclic.

If BM and CN are the perpendiculars drawn on the sides AC and BC of the Delta ABC , prove that the points B, C, M and N are concyclic.

Statement 1 :If the lines 2x+3y+19=0 and 9x+6y-17=0 cut the x-axis at A ,B and the y-axis at C ,D , then the points, A , B , C , D are concyclic. Statement 2 : Since O AxO B=O CxO D , where O is the origin, A , B , C , D are concyclic.

A B C is an isosceles triangle in which A B=A C . If D\ a n d\ E are the mid-points of A B\ a n d\ A C respectively, Prove that the points B ,\ C ,\ D\ a n d\ E are concyclic.

In the rectangular coordinate system shown, ABCD is a parallogram. If the coordinates of the points A,B,C and D are (0,2),(a,b),(a,2) and (0,0), respectively, then b =

There are five points A,B,C,D and E. no three points are collinear and no four are concyclic. If the line AB intersects of the circles drawn through the five points. The number of points of intersection on the line apart from A and B is

ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. Prove that P, Q, C and D are concyclic.

If A, B, C and D are four points such that angleBAC=45^(@) and angleBDC=45^(@) , then A, B, C and D are concyclic.

C_(1):x^(2)+y^(2)=r^(2)and C_(2):(x^(2))/(16)+(y^(2))/(9)=1 interset at four distinct points A,B,C, and D. Their common tangents form a peaallelogram A'B'C'D'. If A'B'C'D' is a square, then the ratio of the area of circle C_(1) to the area of circumcircle of DeltaA'B'C' is

In a square ABCD, show that AC^(2) = 2AB^(2) .