Three circles of equal radii all intersect at a single point . Let the other intersections be , and . Which of the following must be true?
If the vertices of a triangle have rational coordinates, then the coordinates of which of the following are necessarily rational?
(A) Centroid
(B) Circumcenter
(C) Orthocenter
(D) Incenter
Triangle and triangle are directly similar (they have the same orientation). Let the centroids of these two triangles be and , respectively.
If triangle is right, and , then the sum of all possible values of can be expressed as for positive coprime integers .
Find .
Let be a triangle in which . Suppose the orthocentre of the triangle lies on the incircle.
Find .
Consider such that
Let and let be its orthocenter
Let denote circumradius of
Let be inradius and be the exradii of
Then find the value of