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kirichekov

Ответ:

D=20

Пошаговое объяснение:

1. Δ SOA: SO=22, SA=16, OA=R, ∠SAO=α

теорема косинусов:

SO²=SA²+OA²-2·SA·OA·cosα

22²=16²+R²-2·16·R·coaα, -32·R·cosα=484-256-R²

cosalpha= frac{228-R^{2} }{-32R}

2. Δ AOB: OA=OB=R, AB=8, ∠OAB=180°-α (смежные углы)

теорема косинусов:

OB²=OA²+AB²-2·OA·AB·cos(180°-α)

cos(180°-α)= - cosα

OB²=OA²+AB²+2·OA·AB·cosα

R²=R²+8²+2·R·8·cosα, 64+16·R·cosα=0

подставим значение cosα, получим уравнение:

64+16R*frac{228-R^{2} }{-32R} =0

64+frac{228-R^{2} }{-2}=0

R²=100, R=10

D=2·R. D=20

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