MathDB

2

Part of 2008 IMAC Arhimede

Problems(1)

(A_{1}A_{2})(BA_{2}+A_{2}C) +..+(C_{1}C_{2})(AC_{2}+C_{2}B)>3/4

Source: IMAC Arhimede 2008 p2

5/4/2019
In the ABC ABC triangle, the bisector of AA intersects the [BC] [BC] at the point A1 A_ {1} , and the circle circumscribed to the triangle ABC ABC at the point A2 A_ {2} . Similarly are defined B1 B_ {1} and B2 B_ {2} , as well as C1 C_ {1} and C2 C_ {2} . Prove that A1A2BA2+A2C+B1B2CB2+B2A+C1C2AC2+C2B≥34 \frac {A_{1}A_{2}}{BA_{2} + A_{2}C} + \frac {B_{1}B_{2}}{CB_{2} + B_{2}A} + \frac {C_{1}C_{2}}{AC_{2} + C_{2}B} \geq \frac {3}{4}
geometrygeometric inequalityinequalitiesangle bisectorcircumcircle