A triangle is inscribed in a circle of radius 1. The distance between the orthocentre and the circumcentre of the triangle cannot be

Prove that he distance between the circum-centre and the ortho-centre of a triangle ABC is Rsqrt(1-8cosAcos BcosC.

The area of the triangle inscribed in a circle of radius 4 and the ratio of its angles in the ratio 5:4:3 is

Write True or False The incentre and circumcentre of an equilateral triangle are same.

ABC is an isosceles triangle inscribed in a circle of radius rdot If A B=A C and h is the altitude from A to B C , then triangle A B C has perimeter P=2(sqrt(2h r-h^2)+sqrt(2h r)) and area A= ____________ and = __________ and also ("lim")_(h vec 0) A/(P^3)=______

The distance between the circumcentre and orthocentre of the triangle whose vertices are (0,0),(6,8)and (-4,3) is

The isosceles triangle ABC is inscribed in a circle with centre at O. If AP is a diameter of the circle. Then prove that AP is the bisetors of angle BPC .

The circle x^(2)+y^(2)-4x-4y+4=0 is inscribed in a triangle having two of its sides along the coordinate axes. If the locus of the circumcentre of triangle is x+y-xy+k sqrt(x^(2) + y^(2)) = 0 , then k is equal to-

If circumradius of triangle ABC is 4 cm, then prove that sum of perpendicular distances from circumcentre to the sides of triangle cannot exceed 6 cm

In Delta ABC if the orthocentre is (1,2) and the circumcenter is (0,0) then centroid of Delta ABC is.

ABCD be a cycle quadrilateral inscribed in a circle of radius R. The sides of a quadrilateral which can be inscribed in a circle are 6,6,8and 8cm.Then radius of circumcircle is