If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

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.

Equilateral triangles are drawn on the three sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.

If a, b, c are the side of a right triangle where c is the hypotenuse, prove that the radius of the circle which touches all the side of the triangle is given by r= (a+b-c)/2 .

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.

State true or false . The mid point of any diameter of a circle is the centre.

If the bisector of an angle of a triangle also bisects the opposite side, prove that the triangle is isosceles.

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

A line intersecting a circle in two points is called a secant.

The differential equation of circles passing through the points of intersection of unit circle with centre at the origin and the line bisecting the first quadrant, is

For any triangle, prove that the sum of the sides of the triangle is greater than the sum of the medians of the triangle.