If R be the circum radius and r the in radius of a triangle ABC, show that `Rge2r`

In a triangle ABC,r=

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

If circum-radius and in-radius of a triangle ABC be 10 and 3 units respectively , then a cot A +b cot B +c cot C is equal to

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

In an acute angled triangle A B C , a semicircle with radius r_a is constructed with its base on BC and tangent to the other two sides. r_b a n dr_c are defined similarly. If r is the radius of the incircle of triangle ABC then prove that 2/r=1/(r_a)+1/(r_b)+1/(r_c)dot

The angle of elevation of the top of the tower observed from each of three points A,B , C on the ground, forming a triangle is the same angle alpha. If R is the circum-radius of the triangle ABC, then find the height of the tower

In triangle ABC, let angle C = pi//2 . If r is the inradius and R is circumradius of the triangle, then 2(r + R) is equal to

In Delta ABC, a=5, b=4, c=3. G is the centroid of triangle. If R_(1) be the circum radius of triangle GAB then the value of (a)/(65) R_(1)^(2) must be

If R and R' are the circumradii of triangles ABC and OBC, where O is the orthocenter of triangle ABC, then :

If R and R' are the circumradii of triangles ABC and OBC, where O is the orthocenter of triangle ABC, then :