`A C\ a n d\ B D` are chords of a circle which bisect each other. Prove that (i) `A C\ a n d\ B D` are diameters (ii) `A B C D` is a rectangle

A B\ a n d\ C D are two chords of a circle such that A B=6\ c m ,\ C D=12\ c m\ a n d\ A B C Ddot If the distance between A B\ a n d\ C D is 3\ c m , find the radius of the circle.

In figure A B=A C\ a n d\ C P||B A and A P is the bisector of exterior /_C A D of A B C . Prove that /_P A C=/_B C A (ii) A B C P is a parallelogram

In Figure, A D\ a n d\ B E are medians of A B C\ a n d\ B E||D F . Prove that C F=1/4A C

If A B , B C a n d C D are equal chords of a circle with O as centre and A D diameter, then /_A O B= 60^0 (b) 90^0 (c) 120^0 (d) none of these

Diagonals A C a n d B D of a quadrilateral A B C D intersect at O in such a way that a r ( A O D)=a r ( B O C)dot Prove that A B C D is a trapezium.

A B C\ a n d\ D B C are two isosceles triangles on the same bas B C and vertices A\ a n d\ D are on the same side of B C . If A D is extended to intersect B C at P , show that A P bisects "\ "/_A as well as /_D A P is the perpendicular bisector of B C

A B C\ a n d\ D B C are two isosceles triangles on the same bas B C and vertices A\ a n d\ D are on the same side of B C . If A D is extended to intersect B C at P , show that A B D\ ~= A C D (ii) A B P\ ~= A C P

In Figure, A B C D is a parallelogram and X\ a n d\ Y are points on the diagonal B D such that D X=B Y . Prove that A X C Y is a parallelogram (ii) A X=C Y ,\ A Y=C X A Y B\ ~= C X D (iv) A X D~=\ C Y B

In Figure, A B C D is a parallelogram. E\ a n d\ F are the mid-points of the sides A B\ a n d\ C D respectively. Prove that the line segments A F\ a n d\ C E trisect (divide into three equal parts) the diagonal B D .

In a parallelogram A B C D , the bisector of /_A also bisects B C at Xdot Prove that A D=2A B