chord
arc
central angle is times larger than inscribed angle – both intercepting the same arc
Circle Parts Practice Problems - Chords, Arcs & Angles
Master circle geometry with practice problems on chords, arcs, central angles, inscribed angles, and tangents. Build confidence with step-by-step solutions.
📚Practice Circle Components and Properties
- Identify and calculate properties of chords, arcs, and circle segments
- Solve problems involving central angles and inscribed angles relationships
- Apply perpendicular bisector properties from circle center to chords
- Calculate distances between chords and circle centers accurately
- Work with tangent lines and their perpendicular relationships
- Master angle relationships between inscribed and central angles
Understanding The Parts of a Circle
Complete explanation with examples
Circuit Components
Practice The Parts 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 The Parts of a Circle
Step-by-step solutions included
Exercise #1
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
Exercise #2
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 #3
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 #4
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 #5
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:
Frequently Asked Questions
What is the difference between a chord and an arc in a circle?
+A chord is a straight line segment that connects two points on the circle's circumference and passes through the circle. An arc is the curved portion of the circle's circumference between two points and does not pass through the circle - it follows the circle's edge like a rainbow shape.
How do you find the relationship between central and inscribed angles?
+The central angle is always twice the size of an inscribed angle when both angles intercept the same arc. For example, if a central angle measures 60°, the inscribed angle intercepting the same arc will measure 30°.
Is the diameter of a circle considered a chord?
+Yes, the diameter is a special type of chord. It connects two points on the circle's circumference and passes through the center, making it the longest possible chord in any circle.
What happens when you draw a perpendicular from the center to a chord?
+A perpendicular from the circle's center to a chord creates several important properties: 1) It bisects the chord into two equal parts, 2) It forms right angles with the chord, 3) It bisects the central angle subtending that chord, 4) It bisects the arc opposite the chord.
How do you determine if two central angles are equal?
+Two central angles are equal in these cases: Case 1 - When they are subtended by equal arcs, Case 2 - When the chords opposite to the angles are equal in length. Equal central angles also create equal corresponding arcs and chords.
What makes an angle an inscribed angle in a circle?
+An inscribed angle has its vertex located on the circle's circumference (not inside or outside) and its two rays are chords of the circle. The angle 'sits' on the circle's edge and opens toward the interior.
How do tangent lines relate to circle radii?
+A tangent line is always perpendicular to the radius at the point where it touches the circle. This creates a 90° angle between the tangent and radius, and the tangent touches the circle at exactly one point.
What is the distance from a chord to the center of a circle?
+The distance from a chord to the circle's center is the length of the perpendicular line connecting the center to the chord. Equal chords are always at equal distances from the center, and shorter distances indicate longer chords.