Роздiл 5. Коло i круг » 940

Трикутник KLM описано навколо кола з центром О. Знайдіть кути даного трикутника, якщо: 1) ∠OKL = 25°, ∠OLM = 30°; 2) ∠KMO = ∠MKO = 20°; 3) ∠МLO = 2∠OMK = 30°; 4) ∠OLK = ∠OKM = 15°. 1) ∠K = 2∠OKL = 2 • 25° = 50°, ∠L = 2∠OLM = 2 • 30° = 60°, ∠M = 180° – (∠K + ∠L) = 180° – (50° + 60°) = 180° – 110° = 70°; 2) ∠M = 2∠KMO = 2 • 20° = 40°, ∠K = 2∠MKO = 2 • 20° = 40°, ∠L = 180° – (∠M + ∠K) = 180° – (40° + 40°) = 180° – 80° = 100°; 3) ∠L = 2∠MLO = 2 • 30° = 60°, ∠M = 2∠OMK = 30°, ∠K = 180° – (∠M + ∠L) = 180° – (60° + 30°) = 180° – 90° = 90°; 4) ∠L = 2∠OLK = 2 • 15° = 30°, ∠K = 2∠OKM = 2 • 15 = 30°, ∠M = 180° – (∠M + ∠L) = 180° – 60° = 120°.