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

Prove that the distance between the circumcenter and the incenter of triangle ABC is sqrt(R^2-2R r)

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

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

The radii of two circles are R and r unit (R gtr). If the distance between the two centres of the circles be d unit, then prove that the length of their transversal common tangent =sqrt(d^(2) -(R+r)^(2)) unit.

The focal lengths of the objective and the eyepiece of a compound microscope are 1 cm and 5 cm respectively and the distance between the centres of the lenses is 15 cm . If the final image is formed at the least distance of distinct vision , what is the magnifying power of the microscope ?

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line - segment joining the points of contact at the centre.

The co-ordinate of the two verties of a trainge are (15, 0) and (0 ,10): If the co-ordinate of the ortho centre of this triangle is (6, 9),find the co-ordinate of the third vertex of the triangle.

Prove that the centres of three equal circles touchinhg each other are the certices of an equilateral triangle.