Minor Arc, Major Arc, Semicircle

Minor Arc, Major Arc, Semicircle

What is it?

Two points A and B on a circle cut two arcs: the minor (shorter, less than a semicircle) and the major (the long way). A semicircle is half the circumference, sitting on a diameter. Equal central angles (same circle) make equal arcs. Arc measure in degrees equals the central angle in the school treatment.

In simple words

• Two points A and B on a circle cut two arcs: the minor (shorter, less than a semicircle) and the major (the long way).
• MINOR AND MAJOR: Unless AB is a diameter, one arc is minor and one is major.
• SEMICIRCLE: Central angle 180 deg.
• Worked-method reminder: major arc AB = 280 deg

Important terms

MINOR ARC, MAJOR ARC, SEMICIRCLE: Two points A and B on a circle cut two arcs: the minor (shorter, less than a semicircle) and the major (the long way). A semicircle is half the circumference, sitting on a diameter. Equal central angles (same circle) make equal arcs. Arc measure in degrees equals the central angle in the school treatment.

MINOR AND MAJOR: Unless AB is a diameter, one arc is minor and one is major. Naming arc AB without 'minor/major' can be ambiguous; many papers mean the minor. Equal chords sit on equal minor arcs.

SEMICIRCLE: Central angle 180 deg. The bounding chord is a diameter. Angle at the circumference in that semicircle is 90 deg (Chapter 10). Arc length school formula uses fraction of circumference if asked: (theta/360)*2 pi r.

What you should learn

• Explain minor arc, major arc, semicircle using the correct definitions, conditions, and notation.
• Apply minor = shorter, semicircle on a diameter correctly in routine and exam-style questions.
• Show each important step, simplify the result, and check that it satisfies the original conditions.

Examples

• Minor < 180 deg typically
• Major the rest of 360
• Equal chords, equal minor arcs

MINOR AND MAJOR

Unless AB is a diameter, one arc is minor and one is major. Naming arc AB without 'minor/major' can be ambiguous; many papers mean the minor. Equal chords sit on equal minor arcs.

SEMICIRCLE

Central angle 180 deg. The bounding chord is a diameter. Angle at the circumference in that semicircle is 90 deg (Chapter 10). Arc length school formula uses fraction of circumference if asked: (theta/360)*2 pi r.

Full school-level explanation

Two points A and B on a circle cut two arcs: the minor (shorter, less than a semicircle) and the major (the long way). A semicircle is half the circumference, sitting on a diameter. Equal central angles (same circle) make equal arcs. Arc measure in degrees equals the central angle in the school treatment.

Short way, long way, half:

WHAT — MINOR ARC, MAJOR ARC, SEMICIRCLE

Two points A and B on a circle cut two arcs: the minor (shorter, less than a semicircle) and the major (the long way). A semicircle is half the circumference, sitting on a diameter. Equal central angles (same circle) make equal arcs. Arc measure in degrees equals the central angle in the school treatment. The symbols and conditions are part of the mathematics, so include them when stating the rule.

WHY — Why this topic matters

Minor Arc, Major Arc, Semicircle matters because chord and arc theorems convert circle diagrams into equal lengths, equal angles, and right triangles. They are the foundation for later tangent proofs and constructions.

HOW — How to solve and explain it

Start by identifying what is given and what must be found. Work through MINOR AND MAJOR, then SEMICIRCLE. Worked: central angle AOB = 80 deg. Find the major arc AB in degrees. minor arc AB = central angle = 80 deg full circle = 360 deg major arc AB = 360 - 80 major arc AB = 280 deg Finish by checking signs, restrictions, units, and whether the answer matches the question.

MINOR AND MAJOR

Unless AB is a diameter, one arc is minor and one is major. Naming arc AB without 'minor/major' can be ambiguous; many papers mean the minor. Equal chords sit on equal minor arcs.

Remember

• not a diameter => two sizes

Examples

• Minor < 180 deg typically
• Major the rest of 360
• Equal chords, equal minor arcs

SEMICIRCLE

Central angle 180 deg. The bounding chord is a diameter. Angle at the circumference in that semicircle is 90 deg (Chapter 10). Arc length school formula uses fraction of circumference if asked: (theta/360)*2 pi r.

Remember

• diameter cuts two semicircles

Examples

• 180 deg at O
• Chord is diameter
• Rim angle 90

Remember

• minor = shorter
• semicircle on a diameter
• 280 deg
• degrees vs length
• not a diameter => two sizes
• diameter cuts two semicircles
• minor = shorter
• semicircle on a diameter

How the ideas connect

Worked: central angle AOB = 80 deg. Find the major arc AB in degrees. minor arc AB = central angle = 80 deg full circle = 360 deg major arc AB = 360 - 80 major arc AB = 280 deg

Deeper understanding

Go beyond memorising Minor Arc, Major Arc, Semicircle. Connect the definition to reasons, relationships, exceptions, and exam wording.

How the ideas connect

Worked: central angle AOB = 80 deg. Find the major arc AB in degrees. minor arc AB = central angle = 80 deg full circle = 360 deg major arc AB = 360 - 80 major arc AB = 280 deg

Common mistakes

Exam focus

Core Idea

MINOR AND MAJOR

SEMICIRCLE

Worked Method

Exam focus

Quick revision

• minor = shorter
• semicircle on a diameter
• 280 deg
• degrees vs length
• MINOR ARC, MAJOR ARC, SEMICIRCLE: Two points A and B on a circle cut two arcs: the minor (shorter, less than a semicircle) and the maj
• MINOR AND MAJOR: Unless AB is a diameter, one arc is minor and one is major. Naming arc AB without 'minor/major' can

Arc measure in degrees is not the chord length. An 80 deg arc on a huge circle is still 80 deg but a long curve.

For long answers on Minor Arc, Major Arc, Semicircle: define clearly → explain the main parts → give one example → state one exam caution.