MathDB

5

Part of 1975 Polish MO Finals

Problems(1)

R/2r >= 1/ sin a/2 (1- sin a/2)

Source: Polish MO Finals 1975 p5

8/23/2024
Show that it is possible to circumscribe a circle of radius RR about, and inscribe a circle of radius rr in some triangle with one angle equal to aa, if and only if 2Rr≥1sin⁡a2(1−sin⁡a2)\frac{2R}{r} \ge \dfrac{1}{ \sin \frac{a}{2} \left(1- \sin \frac{a}{2} \right)}
geometryGeometric Inequalitiestrigonometry