Prove that the line segment joining the centres of two intersecting circles subtends equal angles at the two points of intersection.

If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.

Line segment joining the centre to any point on the circle is a radius of the circle

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

Recall that two circles are congruent if they have the same radii. Proe that equal chords of congruent circles subtend equal angles at their centres.

Prove that if chords f congruent circles subtend equal angles at their centres, then the chords are equal.

prove that the line segment joining the midpoints of two opposite sides of a parallelogram divides the parallelogram into two parallelograms with equal area.

The line segment joining the mid-points of any two sides of a triangle in parallel to the third side and equal to half of it.

Find the ratio in which the y-axis divides the line segment joining the points (5,-6) and (-1, -4) . Also find the point of intersection.

If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, prove that the chords are equal.