MathDB

10.2

Part of I Soros Olympiad 1994-95 (Rus + Ukr)

Problems(2)

sin a^o = sin a (I Soros Olympiad 1994-95 R2 10.2)

Source:

5/25/2024
Find the smallest positive number aa for which sin⁡ao=sin⁡a\sin a^o = \sin a (on the left (aoa^o) is an angle of aa degrees, on the right is an angle in aa radians).
algebratrigonometry
OA+OB+OC<BC+CA if AB<=BC<=CA (I Soros Olympiad 1994-95 Ukraine R2 10.2)

Source:

6/6/2024
Given a triangle ABCABC and a point OO inside it, it is known that AB≤BC≤CAAB\le BC\le CA. Prove that OA+OB+OC<BC+CA.OA+OB+OC<BC+CA.
geometrygeometric inequality