MathDB

a) (version for grades 10-11)
Let

P

be a point lying in the interior of a triangle. Show that the product of the distances from

P

to the sides of the triangle is at least

8

times less than the product of the distances from

P

to the tangents to the circumcircle at the vertices of the triangle.
b) (version for grades 8-9)
Is it true that for any triangle there exists a point

P

for which equality in the inequality from a) holds?

Problem Statement