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3

Part of 1996 Moldova Team Selection Test

Problems(1)

Prove that $\frac{\sin(B+C)}{\sin B \cdot \sin C} \geq \frac{2}{3}.$

Source: Moldova TST 1996

8/8/2023
In triangle ABCABC medians from BB and CC are perpendicular. Prove that sin⁡(B+C)sin⁡B⋅sin⁡C≥23.\frac{\sin(B+C)}{\sin B \cdot \sin C} \geq \frac{2}{3}.
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