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.

Angle of intersection of two circles is given by :

The maximum number of points of intersection of 7 circles is

Prove that the circle drawn with any side of a rhombus as diameter, passes through the point of intersection of its diagonals.

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.

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.

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

The lengths of two sides of a triangle are 12cm and 15cm. Between what two measures should the length of the third side fall?

The equilateral triangles are drawn on the sides of a right triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of the triangles on the other two sides. OR In the given figure, PA, QB and RC are each perpendicular to AC. Prove that 1/x+1/z=1/y

"If the square on the longest sides of a triangle is equal to the sum of the squares on the other two sides then those two sides contain a right angle." Prove.

What is the name given to a line intersecting a circle in two points ?