A chord in a circle is a straight line that connects any points that are on the circle.
• The chord passes inside the circle and not over it.
• The longest chord in the circle is the diameter
• The radius is not a chord.
Circle Chords Practice Problems and Solutions Online
Master circle chords with step-by-step practice problems. Learn to identify chords, distinguish from radius and diameter, and solve geometry problems.
📚Master Circle Chords Through Interactive Practice
- Identify chords correctly in various circle diagrams and real-world examples
- Distinguish between chords, radius, and diameter with confidence
- Understand why diameter is the longest chord in any circle
- Solve problems involving chord properties and measurements
- Apply chord concepts to guitar strings and other practical situations
- Calculate chord lengths using circle geometry principles
Understanding Chords of a Circle
Complete explanation with examples
Practice Chords of a Circle
Test your knowledge with 6 quizzes
Calculate the length of the arc marked in red given that the circumference is 12.
Examples with solutions for Chords of a Circle
Step-by-step solutions included
Exercise #1
In which of the circles is the point marked inside of the circle and not on the circumference?
Step-by-Step Solution
Let's remember that the circular line draws the shape of the circle, and the inner part is called a disk.
Therefore, in diagram B, the point is located in the inner part, meaning inside the disk.
Answer:
Video Solution
Exercise #2
Identify which diagram shows the radius of a circle:
Step-by-Step Solution
Remember that a radius is a line segment connecting the center of a circle to any point on the circle itself.
In drawing C we can see that the line coming from the center of the circle indeed connects to a point on the circle itself, while in the other drawings the lines don't touch any point on the circle.
Therefore, C is the correct drawing.
Answer:
Exercise #3
Identify which diagram shows the radius of a circle:
Step-by-Step Solution
Remember that a radius is a line segment connecting the center of the circle to a point that lies on the circle itself.
In drawing A, the line doesn't touch any point on the circle itself.
In drawing B, the line doesn't pass through the center of the circle.
We can see that in drawing C, the line that extends from the center of the circle is indeed connected to a point on the circle itself.
Answer:
Video Solution
Exercise #4
Where does a point need to be so that its distance from the center of the circle is the shortest?
Step-by-Step Solution
Let's remember that the circle is actually the inner part of the circumference, meaning the enclosed area within the frame of the circumference.
Therefore, a point whose distance is less than the radius from the center of the circle will necessarily be inside the circle.
Answer:
Inside
Exercise #5
A point whose distance from the center of the circle is _______ than the radius, is outside the circle.
Step-by-Step Solution
Let's remember that the circle is actually the inner part of the circumference, meaning the enclosed area within the frame of the circumference.
Therefore, a point whose distance is greater than the center of the circle will necessarily be outside the circle.
Answer:
greater
Frequently Asked Questions
What is a chord in a circle and how do you identify it?
+A chord is a straight line that connects any two points on a circle's circumference, passing through the circle's interior. To identify a chord, look for a line segment with both endpoints touching the circle's edge, but not necessarily passing through the center.
Is the diameter of a circle considered a chord?
+Yes, the diameter is a special type of chord that passes through the center of the circle. It is the longest possible chord in any circle, connecting two points on opposite sides of the circumference.
Why is the radius not a chord in circle geometry?
+The radius is not a chord because it connects the center of the circle to a point on the circumference, rather than connecting two points on the circle's edge. A chord must have both endpoints on the circle's boundary.
How do you find the length of a chord in a circle?
+Chord length can be calculated using the formula: Chord = 2r × sin(θ/2), where r is the radius and θ is the central angle. You can also use the Pythagorean theorem if you know the perpendicular distance from the center to the chord.
What are some real-world examples of chords in circles?
+Common examples include guitar strings stretched across the sound hole, bridge cables spanning circular arches, spokes on bicycle wheels (though these are radii), and any straight line drawn across circular objects like pizza slices or clock faces.
How many chords can you draw in a circle?
+You can draw infinitely many chords in a circle. Any two distinct points on the circle's circumference can be connected to form a chord, and since there are infinitely many points on a circle, there are infinitely many possible chords.
What is the difference between a chord and a secant line?
+A chord is a line segment with both endpoints on the circle, while a secant is a line that intersects the circle at two points but extends beyond the circle. The chord is the portion of the secant line that lies within the circle.
Can two chords in a circle be parallel to each other?
+Yes, two chords can be parallel to each other. Parallel chords in a circle are equidistant from the center, and if they have the same length, they will be the same distance from the center on opposite sides.