State the type of circle which touches all the sides of a triangle and the circle passing through all the vertices of a triangle.

The radius of the circle passing through the vertices of the triangle ABC,is

What is the number of circles passing through all the vertices of a given triangle ?

Consider a triangle Delta whose two sides lies on the x-axis and the line x+y+1=0 . If the orthocenter of Delta is (1,1) , then the equation of the circle passing through the vertices of the triangle is

The equation of a circle with the origin as the centre and passing through the vertices of an equilateral triangle whose altitude is of length 3 units is

A circle touches all sides of quadrilateral ABCD then which one of these is true :

A circumcircle is a circle which passes through all vertices of a triangle and an incircle is a circle which is inscribed in a triangle touching all sides of a triangle. Let ABC be a right-angled triangle whose radius of the circumcircle is 5 and its one side AB = 6. The radius of incircle of triangle ABC is r. Area of Delta ABC is

(0,0) is the centre of the circle passing through the vertices of an equilateral triangle. If the length of the median of the triangle is 9 units then equation of the circle is

A circle touches all sides of a parallelogram. So the parallelogram must be a

The radical center of the three circles described on the sides of a triangle as diameters is the orthocenter of a triangle.

A circumcircle is a circle which passes through all vertices of a triangle and an incircle is a circle which is inscribed in a triangle touching all sides of a triangle. Let ABC be a right angled triangle whose radius of circumcircle is 5 and its one side AB = 6. The radius of incircle of triangle ABC is r. The value of r is