Вопрос:

Analyze the three cases of the relationship between a line and a circle. Complete the table based on the given conditions (OH > R, OH = R, OH < R), describing the number of common points and the name of the line 'a'.

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Ответ:

Analysis of Cases:

We are given a line 'a' and a circle with center O and radius R. We are also given that OH is perpendicular to line 'a', and H is a point on line 'a'. The relationship between the distance from the center to the line (OH) and the radius (R) determines how the line and circle interact.

ConditionCommon PointsName of Line 'a'
OH > RНе имеют общих точекНе пересекает окружность
OH = RТолько одну общую точкуКасательная
OH < RДве общие точкиСекущая

Answer: The table above summarizes the analysis.

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