Learn about Circles through these example problems with detailed step-by-step solutions.
Example 1: Identifying Parts of a Circle
Identify the Center, Radius, and Diameter in the given circle diagram.
Step 1: Observe the diagram of the circle.
Step 2: The **Center** is the fixed point exactly in the middle of the circle. It is usually labeled with a point.
Step 3: A **Radius** is a line segment from the Center to any point on the boundary of the circle. Look for such a line segment.
Step 4: A **Diameter** is a line segment that passes through the Center and connects two points on the boundary of the circle. It is the longest chord. Look for such a line segment.
Step 5: Based on the labels in the diagram (assuming standard labels like O for Center, OA for Radius, BC for Diameter):
Center: Point O
Radius: Line segment OA (or any line segment from O to the boundary)
Diameter: Line segment BC (or any line segment passing through O and connecting two points on the boundary)
Example 2: Relationship between Radius and Diameter
If the radius of a circle is 5 cm, what is its diameter?
Step 1: Understand the relationship between the radius and the diameter of a circle.
Step 2: The diameter of a circle is always twice the length of its radius. The formula is: Diameter = $2 \times$ Radius.
Step 3: The given radius is 5 cm.
Step 4: Substitute the value of the radius into the formula: Diameter = $2 \times 5$ cm.
Step 5: Calculate the diameter: Diameter = 10 cm.
Step 6: Therefore, if the radius of a circle is 5 cm, its diameter is 10 cm.
Example 3: Drawing a Circle with a Compass
Draw a circle with a radius of 3 cm.
Step 1: Gather your tools: a pencil, a ruler, and a compass.
Step 2: Use the ruler to set the distance between the pencil tip and the compass point to 3 cm. This distance is the radius.
Step 3: Choose a point on your paper where you want the center of the circle to be. Place the sharp point of the compass on this point. This point is the center.
Step 4: Hold the compass by the top and rotate it carefully, keeping the sharp point fixed on the center. The pencil tip will draw the circle.
Step 5: You have now drawn a circle with a radius of 3 cm.
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Related Concepts
Explore these related mathematical concepts to deepen your understanding of circles.
Center
The fixed point from which all points on the circle are equidistant.
Radius
A line segment connecting the center of the circle to any point on its boundary. It is half the length of the diameter.
Diameter
A line segment passing through the center of the circle and connecting two points on its boundary. It is twice the length of the radius.
Circumference
The distance around the boundary of the circle.
Chord
A line segment connecting any two points on the boundary of the circle.
Arc
A part or segment of the circumference of a circle.