MathDB

4

Part of 2022 Swedish Mathematical Competition

Problems(1)

EF x CI / 2 >= [ ABC ]

Source: 2022 Swedish Mathematical Competition p4

3/24/2024
Let ABCABC be an acute triangle. Let II be a point inside the triangle and let DD be a point on the line ABAB. The line through DD which is parallel to AIAI intersects the line ACAC at the point EE, and the line through DD parallel to BIBI intersects the line BCBC in point FF. prove that EF⋅CI2≥area(△ABC)\frac{EF \cdot CI}{2} \ge area (\vartriangle ABC)
geometrygeometric inequality