Problems

Age
Difficulty
Found: 6

Prove that the segment connecting the vertex of an isosceles triangle to a point lying on the base is no greater than the lateral side of the triangle.

Prove that \((a + b - c)/2 < m_c < (a + b)/2\), where \(a\), \(b\) and \(c\) are the lengths of the sides of an arbitrary triangle and \(m_c\) is the median to side \(c\).

Prove that \(\angle ABC < \angle BAC\) if and only if \(AC < BC\), that is, the larger side lies opposite the larger angle of the triangle, and opposite the larger side lies the larger angle.