Mathematics
Grade 10
15 min
Parts of a circle
Parts of a circle
What you'll learn
- Identify and label the radius, diameter, chord, arc, and center of a circle with 100% accuracy on a worksheet.
- Explain the relationship between the radius and diameter of a circle, using mathematical terms, in a written paragraph with at least 3 sentences.
- Apply the formulas for radius (r = d/2) and diameter (d = 2r) to solve for the missing measurement of a circle in 8 out of 10 word problems.
- Distinguish between a chord and a diameter, providing a clear explanation of their similarities and differences using geometric vocabulary.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify and define the key parts of a circle: radius, diameter, chord, secant, and tangent.
Differentiate between a major arc, a minor arc, and a semicircle based on their measures.
Define and identify central angles and inscribed angles and their corresponding intercepted arcs.
Apply the relationship between a central angle and its intercepted arc to find unknown measures.
Apply the Inscribed Angle Theorem to find unknown angle or arc measures.
Use the Tangent-Radius Theorem to solve problems, often in conjunction with the Pythagorean theorem.
Ever wondered how a pizza is perfectly cut or how satellites maintain their orbit around the Earth? 🍕 It all comes down to understanding the fundamental parts of a circle!
This tutorial will dissect the circle,...
2
Key Concepts & Vocabulary
TermDefinitionExample
Radius (r)A line segment from the center of a circle to any point on the circle. All radii of a given circle are congruent.In a circle with center O, if A is a point on the circle, then the segment OA is a radius.
ChordA line segment whose endpoints both lie on the circle. The diameter is the longest possible chord of a circle.If points B and C are on a circle, the line segment BC is a chord.
Diameter (d)A chord that passes through the center of the circle. Its length is twice the length of the radius.If chord BC passes through the center O, then BC is a diameter.
SecantA line that intersects a circle at exactly two points. It contains a chord.A line that passes through points D and E on a circle is a secant line.
TangentA line in the plane of a circle that intersect...
3
Core Formulas
Diameter-Radius Relationship
d = 2r
The diameter (d) of a circle is always twice the length of its radius (r). Use this to convert between the two fundamental measures of a circle's size.
Central Angle-Arc Measure Theorem
m∠AOB = m(arc AB)
The measure of a central angle (in degrees) is equal to the measure of its intercepted arc. This provides a direct link between an angle at the center and a portion of the circumference.
Inscribed Angle Theorem
m∠ABC = \frac{1}{2} m(arc AC)
The measure of an inscribed angle is exactly half the measure of its intercepted arc. This is a crucial theorem for finding angles when the vertex is on the circle, not at the center.
Tangent-Radius Theorem
A tangent line is perpendicular (⊥) to the radius at the point of tangency....
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Challenging
In circle P, the measure of inscribed angle ∠ABC is (2x + 7)° and the measure of its intercepted arc AC is (5x + 5)°. Find the measure of ∠ABC.
A.50°
B.9°
C.45°
D.25°
Challenging
In circle O, the measure of central angle ∠MON is (5x - 10)° and its intercepted arc MN is (4x + 12)°. What is the measure of ∠MON?
A.22°
B.100°
C.88°
D.112°
Challenging
Line AB is tangent to circle C at point B. The radius of the circle is 6 units and the distance from the external point A to the center C is 12 units. What is the measure of ∠ACB?
A.30°
B.45°
C.90°
D.60°
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Frequently asked questions
What grade level is "Parts of a circle"?
Parts of a circle is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Parts of a circle?
You'll be able to: Identify and label the radius, diameter, chord, arc, and center of a circle with 100% accuracy on a worksheet; Explain the relationship between the radius and diameter of a circle, using mathematical terms, in a written….
Is "Parts of a circle" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Parts of a circle?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.