Properties of Circles
Table Of Contents
🎬 Math Angel Video: Circles and Key Concepts Explained
What are Key Properties of a Circle?
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- 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. $$\large d = 2r$$ - 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?
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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.
🍪 Quiz: Practice Radius, Chords, Tangents
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