Question 16
a. Given five points on a plane such that no three of the points are collinear, show that among the triangles which are drawn using any three of these five points as vertices, at least three of the triangles formed are not acute-angled triangles. (An acute-angled triangle is one in which all the three interior angles are acute angles.)
b. Given any 100 points on a plane such that no three of the points are collinear, show that among the triangles which are drawn using any three of these 100 points as vertices, at least 30% of the triangles are not acute-angled triangles.
b. Given any 100 points on a plane such that no three of the points are collinear, show that among the triangles which are drawn using any three of these 100 points as vertices, at least 30% of the triangles are not acute-angled triangles.