The square is inscribed in the circle. Column A: The length of a diagonal of the square Column B: The length of a diameter of the circle
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Drawing a quick sketch for geometry problems is often the fastest way to see the relationship between the parts. As soon as you draw a square inside a circle, you'll notice the diagonal and diameter are the same line.
The relationship cannot be determined from the information given.
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The Correct Option isC
Solution and Explanation
Step 1: Understanding the Concept:
The term "inscribed" means that the square is drawn inside the circle in such a way that all four of its vertices (corners) touch the circumference of the circle. Step 2: Detailed Explanation:
Let's visualize the figure described. We have a circle with a square perfectly fitted inside it.
\begin{itemize}
\item A diameter of a circle is a straight line segment that passes through the center of the circle and whose endpoints lie on the circle.
\item A diagonal of a square is a straight line segment connecting two opposite vertices.
\end{itemize}
When a square is inscribed in a circle, its vertices are on the circle's circumference. The diagonal of the square connects two of these opposite vertices. Because the angles of a square are 90 degrees and the vertices are on the circle, the diagonal must subtend a 180-degree arc, meaning it must pass through the center of the circle. A line segment that connects two points on the circle and passes through the center is, by definition, a diameter.
Therefore, the diagonal of the inscribed square is also a diameter of the circle. Step 3: Final Answer:
The length of a diagonal of the square is equal to the length of a diameter of the circle. The two quantities are equal.
