In a triangle ABC, AD, BE and CF are the altitudes and R is the circum radius, then the radius of the circle DEF is

AL, BM and CN are perpendicular from angular points of a triangle ABC on the opposite sides BC, CA and AB respectively. Delta is the area of triangle ABC, (r ) and R are the inradius and circumradius. Radius is the circum circle of Delta LMN is

In an acute angled triangle ABC , let AD, BE and CF be the perpendicular opposite sides of the triangle. The ratio of the product of the side lengths of the triangles DEF and ABC , is equal to

Find the ratio of the circum-radius and the inradius of DeltaABC, whose sides are in the ratio 4:5:6.

In an acute angle Delta ABC, let AD, BE and CF be the perpendicular from A, B and C upon the opposite sides of the triangle. (All symbols used have usual meaning in a tiangle.) The circum-radius of the Delta DEF can be equal to

In an acute angle Delta ABC, let AD, BE and CF be the perpendicular from A, B and C upon the opposite sides of the triangle. (All symbols used have usual meaning in a tiangle.) The orthocentre of the Delta ABC, is the

If R be circum-radius of DeltaABC, then circum-radius of a pedal Delta is

In an equilateral triangle show that the in-radius and the circum-radius are connected by r =R/2.

If the altitudes of a triangle be 2,4,6, then find its in-radius.

AD,BE and CF the altitudes of triangleABC are equal, prove that triangleABC is equilateral.

In triangle ABC, medians AD and CE are drawn AD = 5, angle DAC = pi//8, and angle ACE = pi//4 , then the area of the triangle ABC is equal to