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What is a Minor Arc?
Grade Level:
Class 6
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
A minor arc is the shorter part of the circumference of a circle between two points on the circle. Imagine you cut a circle at two points; the smaller piece of the curve you get is the minor arc. It always measures less than 180 degrees.
Simple Example
Quick Example
Think of a round pizza cut into slices. If you take two points on the crust, the smaller curved edge between these two points is a minor arc. For instance, if a pizza is cut into 8 equal slices, the crust of one slice is a minor arc.
Worked Example
Step-by-Step
Let's say a circular clock face has points A and B. The angle formed at the center of the clock by lines going to A and B is 90 degrees.
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Step 1: Identify the two points on the circle (A and B).
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Step 2: Find the angle subtended by these points at the center of the circle. Here, it's 90 degrees.
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Step 3: Since 90 degrees is less than 180 degrees, the arc connecting A and B that corresponds to this 90-degree angle is a minor arc.
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Answer: The arc is a minor arc because its central angle is 90 degrees, which is less than 180 degrees.
Why It Matters
Understanding minor arcs is crucial in fields like engineering and architecture for designing curved structures and calculating material needs. It's also used in computer graphics for drawing smooth curves and in physics to describe the path of objects moving in a circular motion, like satellites orbiting Earth.
Common Mistakes
MISTAKE: Confusing a minor arc with a major arc or a semicircle. | CORRECTION: A minor arc is always the SHORTER arc between two points, and its central angle is always less than 180 degrees.
MISTAKE: Thinking the arc length is the straight line distance between the two points. | CORRECTION: The arc is the curved path along the circle's edge, not the straight line (chord) connecting the points.
MISTAKE: Measuring the arc in linear units (like cm) instead of angular units (degrees) when talking about its 'measure'. | CORRECTION: The 'measure' of a minor arc is the measure of the central angle it subtends, in degrees. Its 'length' is in linear units.
Practice Questions
Try It Yourself
QUESTION: If two points on a circle form an angle of 60 degrees at the center, is the arc between them a minor arc? | ANSWER: Yes, because 60 degrees is less than 180 degrees.
QUESTION: A circular bangle is broken into two pieces. One piece makes an angle of 200 degrees at the center. What type of arc is the other piece? | ANSWER: The other piece will form an angle of 360 - 200 = 160 degrees at the center. Since 160 degrees is less than 180 degrees, it is a minor arc.
QUESTION: A car's wheel rotates. If a specific point on the tire travels a path that makes a 120-degree angle at the center of the wheel, what kind of arc has it traced? | ANSWER: It has traced a minor arc because 120 degrees is less than 180 degrees.
MCQ
Quick Quiz
Which of these describes a minor arc?
An arc that covers exactly half of a circle.
The shorter arc between two points on a circle.
An arc that measures more than 180 degrees.
A straight line segment connecting two points on a circle.
The Correct Answer Is:
B
A minor arc is defined as the shorter of the two arcs formed by two points on a circle, and its central angle is always less than 180 degrees. Options A and C describe a semicircle and a major arc respectively, while option D describes a chord.
Real World Connection
In the Real World
When you see the curved boundary of a cricket ground, or the arch of a bridge over a river, parts of these curves can often be described as minor arcs. Even the path a satellite takes around a small portion of Earth can be modeled as a minor arc in certain calculations by ISRO scientists.
Key Vocabulary
Key Terms
CIRCLE: A round shape where all points are equally distant from the center. | CIRCUMFERENCE: The total distance around the edge of a circle. | CENTRAL ANGLE: The angle formed at the center of a circle by two radii. | RADIUS: A line segment from the center of a circle to any point on its circumference.
What's Next
What to Learn Next
Now that you understand minor arcs, you can learn about major arcs and semicircles. Then, you can explore how to calculate the actual length of these arcs, which is super useful in many practical situations!
