Arcs and chords

Key Notes :

🔵 Circle Basics

• A circle is a round shape with all points equidistant from the center.
• 👉 That equal distance is called the radius.

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🟢 What is a Chord?

• A chord is a line segment joining any two points on a circle.
• 👉 Every diameter is the longest chord in a circle.
• 👉 All diameters are chords, but not all chords are diameters.
• Example: Line AB inside a circle but not through center = chord.

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🟣 What is an Arc?

An arc is a part (portion) of the circle’s circumference.

Two types:

• Minor arc: smaller arc (less than 180°) 🌙
• Major arc: bigger arc (more than 180°) 🌕

The arc is usually named by two points on the circle.

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🔶 Relationship Between Chords and Arcs

• Equal chords subtend (form) equal arcs.
• Equal arcs subtend equal chords.
• 👉 Bigger chord = bigger arc, smaller chord = smaller arc.

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🔵 Perpendicular from Center to a Chord

• If you draw a perpendicular from the center of the circle to a chord,
  👉 it bisects the chord (cuts it into two equal parts). ✂️

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🟩 Equal Distance Property

• Chords that are equidistant from the center are equal in length.
• The nearer a chord is to the center, the longer it becomes.

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🟠 Angle and Arc Relationship

• The central angle (angle at the center) formed by two radii equals the measure of the arc it intercepts.
  👉 Example: A central angle of 60° makes an arc of 60°.

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🟣 Important Terms

• Radius (r): center → any point on circle
• Diameter (2r): longest chord
• Circumference: distance around the circle
• Center: the middle point of the circle

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🌟 Real-Life Applications

• Arcs appear in bridges, wheels, windows, rainbows, and more. 🌈🚲
• Chords are used for construction, design, and geometry in engineering.

Learn with an example

let’s practice!