Prove that the line segment joining the points of contact of two parallel tangents of a circle, passes through its centre.

Prove that the segment joining the point of contact of two parallel tangents passes through the centre.

Prove that the line joining the mid-points of two parallel chords of a circle passes through the centre.

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

Direction ratio of the line segment joining two points

Prove that the line joining the mid-point of a chovd to the centre of the circle passes through the mid-point of the corresponding minor arc.

Prove that the line segment joining the mid points of two sides of a triangle is parallel to its third side.

At any point (x,y) of a curve,the slope of the tangent is twice the slope of the line segment joining the point of contact to the point Find the equation of the curve given that it passes through quad (-2,1)

Prove that the line segment joining the mid points of two side of a triangle is parallel to the third side and equal to half of it.

Prove that the line segment joining the mid- points of the diagonals of a trapezium is parallel to each of the parallel sides and is equal to half the difference of these sides.

Prove that the segment joining the middle points of two non-parallel sides of a trapezium is parallel to the parallel sides and half of their sum.