Maths Olympiad Exam

Let ABC be a triangle. An interior point P of ABC is said to be good if we can find exactly 27 rays emanating from P intersecting the sides of the triangle ABC such that the triangle is divided by these rays into 27 smaller triangles of equal area. Determine the number of good points for a given triangle ABC.

Read Solution (Total 0)

Maths Olympiad Other Question

Let ABC be an acute-angled triangle, and let D, E, F be points on BC, CA, AB respectively such that AD is the median, BE is the internal angle bisector and CF is the altitude. Suppose FDE = C, DEF = A and EFD = B. Prove that ABC is equilateral. Let ABCD be a quadrilateral inscribed p in a circle. Suppose AB = 2 + p2 and AB subtends 135 at the centre of the circle. Find the maximum possible area of ABCD