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Рассмотрим треугольник АВО: угол В равен 90° (радиус всегда перпендикулярен касательной).

ОВ = 24 (радиус окружности), АВ = 32 (по условию). Найдем длину гипотенузы ОА по теореме Пифагора:

ОА = √(OB² + AB²) = √(24² + 32²) = √(576 + 1024) = √1600 = 40.

Отрезок ОА состоит из двух отрезков ОD и AD: OA = OD + AD. OD является радиусом окружности, значит, OD = 24.

Значит, отрезок AD = OA - OD = 40 - 24 = 16.

ответ: длина AD равна 16.

Объяснение:

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