Mathematics
Grade 10
15 min
Find the radius of a circle
Find the radius of a circle
What you'll learn
- Solve one-step multiplication word problems involving 1-digit numbers with 80% accuracy.
- Identify the multiplication operation needed to solve a word problem involving groups and equal amounts in at least 4 out of 5 word problems.
- Explain the strategy used to solve a multiplication word problem using mathematical vocabulary (e.g., product, factor, times) in a complete sentence at least once.
- Apply multiplication to solve real-world problems involving arrays, equal groups, and comparison statements with 75% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Find the radius of a circle given its center and a point on the circle.
Determine the radius of a circle from its equation in standard form, (x - h)² + (y - k)² = r².
Find the radius of a circle by converting its equation from general form to standard form using the method of completing the square.
Calculate the radius of a circle given the two endpoints of a diameter.
Apply the Distance Formula as a primary tool for finding the radius.
Explain the relationship between the radius, center, and the equation of a circle.
How does your phone's GPS know your exact location using signals from satellites orbiting high above? 🛰️ It all comes down to circles and their radii!
In this tutorial, you will master several methods for finding the radius, a critical...
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Key Concepts & Vocabulary
TermDefinitionExample
CircleThe set of all points in a plane that are at a fixed distance from a fixed point. The fixed point is the center, and the fixed distance is the radius.All points that are exactly 5 units away from the point (2, 3).
Center (h, k)The fixed point from which all points on the circle are equidistant.In the equation (x - 4)² + (y + 1)² = 25, the center is (4, -1).
Radius (r)The distance from the center of the circle to any point on the circle. It is always a positive value.If a circle has its center at (0, 0) and the point (3, 4) is on the circle, the radius is 5 units.
DiameterA line segment that passes through the center of the circle and has its endpoints on the circle. Its length is twice the radius (d = 2r).If a circle's radius is 6, its diameter is 12.
Stan...
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Core Formulas
The Distance Formula
r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
Use this to find the radius (r) when you know the coordinates of the center (x₁, y₁) and any point on the circle (x₂, y₂). The radius is simply the distance between these two points.
The Standard Equation of a Circle
(x - h)^2 + (y - k)^2 = r^2
Use this to find the radius when the circle's equation is given in standard form. The radius 'r' is the square root of the constant term on the right side of the equation.
The Midpoint Formula
Center (h, k) = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})
This isn't for the radius directly, but it's a crucial first step. Use it to find the center of the circle if you are given the endpoints of a diameter, (x₁, y₁) and (x₂, y₂). Once you have the...
5 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Challenging
A circle has its center on the x-axis and passes through the points A(1, 4) and B(7, 4). What is the radius of the circle?
A.3
B.4
C.5
D.6
Challenging
The circle given by x² + y² - 10x + 4y + F = 0 passes through the point (1, 1). What is the radius of this circle?
A.25
B.√29
C.4
D.5
Challenging
What is the radius of a circle whose diameter is the line segment connecting the centers of the circles (x-2)²+(y-3)²=9 and (x+4)²+(y+5)²=16?
A.10
B.5
C.100
D.√50
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Frequently asked questions
What grade level is "Find the radius of a circle"?
Find the radius of a circle is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Find the radius of a circle?
You'll be able to: Solve one-step multiplication word problems involving 1-digit numbers with 80% accuracy; Identify the multiplication operation needed to solve a word problem involving groups and equal amounts in at least 4 out of 5 word….
Is "Find the radius 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 Find the radius of a circle?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.