Properties of Circles
🎬 Video: Understanding Circles
What is a Circle? (0:01)
A circle is a perfectly round shape where every point on its edge is the same distance from the center. This distance is called the radius.
Circles are everywhere in real life. For example, bike wheels are circular because their round shape prevents bumps as you ride, ensuring a comfortable journey.
What are Key Properties of a Circle? (0:30)
- The radius is a line segment from the center to any point on the circle.
- The diameter is a line passing through the center, connecting two points on the circle.
The diameter is always twice the radius. $$d=2r$$ - A chord is a line segment with both endpoints on the circle.
The longest chord in a circle is the diameter. - An arc is a part of the circumference of the circle.
- A sector is a region enclosed by two radii and the arc between them.
A sector is shaped like a “pizza slice”. - A segment is a part of the circle enclosed by a chord and the arc above it.
- A tangent is a straight line that touches the circle at exactly one point and is perpendicular to the radius at that point.
How to Use Circles to Find Specific Points? (1:30)
Task:
Find all points that are 5 cm away from $P_A$ and 3 cm away from $P_B$.
Approach:
- Draw a circle with a 5 cm radius centered at $P_A$.
- Draw another circle with a 3 cm radius centered at $P_B$
Solution:
The points where the two circles intersect are exactly 5 cm from $P_A$ and 3 cm from $P_B$
Application:
This method is useful in geometry, navigation, engineering, and design.
📂 Flashcards: Parts of a Circle
🍪 Quiz: Practice Radius, Chords, Tangents and More
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