Prove that the line segment obtained by joining the two circles bisects the common chord of the circles at right angle.

Prove that the line segment obtained by joining the points (1,2) and (-2,-4) passes through the origin.

Prove that the line segment obtianed by joining the midpoints of two transversed sides of a trapezium is parallel to the parallel sides of the trapezium.

Prove that the mid-point of the lines segments obatained by joining the points (2,1) and (6,5) lies on the line obtained by joining the points (-4,-5) and (9,8).

The angle in the segment of a circle which is less than a semi circle is an obtuse angle.

Which of the following statements are true and which are false? In each case give a valid reason for saying so. The centre of a circle bisects each chord of the circle

Prove analytically that the straight line joining the middle point of a chord of a circle with the centre is perpendicular to the chord.

Prove that diameter is the greatest chord of a circle.

Prove that the perpendicualr bisector of any chord of a circle passes thorugh the centre of the circle .

Show that the line segments joining the midpoints of the opposite sides of a quadrilateral and bisect each other.

Prove that the line segment joining the mid-point of two transverse sides of a trapezium is parallel to its parallel sides.