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103 LearnersLast updated on September 13, 2025
Tangent of a Circle Calculator
Calculators are reliable tools for solving simple mathematical problems and advanced calculations like trigonometry. Whether you’re cooking, tracking BMI, or planning a construction project, calculators will make your life easy. In this topic, we are going to talk about the tangent of a circle calculator.
What is a Tangent of a Circle Calculator?
A tangent of a circle calculator is a tool used to find the length of the tangent from a point outside the circle to the point where it touches the circle. The tangent is a straight line that touches the circle at exactly one point, making it perpendicular to the radius at that point.
This calculator simplifies the process of finding tangents, saving time and effort.
How to Use the Tangent of a Circle Calculator?
Given below is a step-by-step process on how to use the calculator:
Step 1: Enter the radius of the circle: Input the radius of the circle into the given field.
Step 2: Enter the distance from the center of the circle to the external point: Input the distance into the given field.
Step 3: Click on calculate: Click on the calculate button to get the tangent length.
Step 4: View the result: The calculator will display the result instantly.
How to Calculate the Tangent of a Circle?
To calculate the tangent length from an external point to a circle, the calculator uses the Pythagorean theorem.
If 'r' is the radius, 'd' is the distance from the center to the external point, then the tangent length 't' is given by: t = √(d² - r²)
This formula helps determine the length of the tangent by finding the difference between the square of the distance and the square of the radius and then taking the square root.
Tips and Tricks for Using the Tangent of a Circle Calculator
When using a tangent of a circle calculator, there are a few tips and tricks to make it easier and avoid mistakes:
Ensure the distance from the center to the external point is greater than the radius.
Otherwise, the tangent does not exist.
Visualize the circle and the tangent line to understand the relationship.
Double-check your input values to ensure accuracy.
Common Mistakes and How to Avoid Them When Using the Tangent of a Circle Calculator
We may think that when using a calculator, mistakes will not happen. But it is possible to make errors when using a calculator.
Mistake 1
Confusing the radius and the distance from the center.
Ensure you do not swap the radius with the distance from the center. The radius is always less than the distance from the center to any external point.
Mistake 2
Entering a distance from the center less than the radius.
If the distance from the center to the external point is less than the radius, the tangent cannot be calculated as it does not exist.
Mistake 3
Misinterpreting the result of the calculation.
Remember, the result shows the length of the tangent from the external point to the circle, which is a straight line tangential to the curve.
Mistake 4
Relying solely on the calculator without understanding the geometry.
While the calculator provides quick results, understanding the underlying geometric principles ensures more accurate and meaningful interpretations.
Mistake 5
Assuming the calculator handles all types of circles.
The calculator assumes a perfect circle. For shapes that are not perfect circles, the results may not apply.
Tangent of a Circle Calculator Examples
Problem 1
Find the length of the tangent from a point 10 units away from the center of a circle with a 6-unit radius.
Use the formula:
t = √(d² - r²) t = √(10² - 6²)
t = √(100 - 36)
t = √64
t = 8 The tangent length is 8 units.
Explanation
By applying the formula, we find the tangent length by subtracting the square of the radius from the square of the distance and taking the square root.
Problem 2
A circle has a radius of 5 units, and a point is located 13 units from the center. What is the tangent length?
Use the formula:
t = √(d² - r²)
t = √(13² - 5²)
t = √(169 - 25)
t = √144
t = 12 The tangent length is 12 units.
Explanation
Using the formula, we calculate the tangent length by finding the square root of the difference between the square of the distance and the square of the radius.
Problem 3
If a point is located 15 units from the center of a circle with a radius of 9 units, determine the length of the tangent.
Use the formula:
t = √(d² - r²)
t = √(15² - 9²)
t = √(225 - 81)
t = √144
t = 12 The tangent length is 12 units.
Explanation
The calculation involves using the Pythagorean theorem, subtracting the square of the radius from the square of the distance, and taking the square root to find the tangent length.
Problem 4
What is the tangent length from a point 30 units away from the center of a circle with a 24-unit radius?
Use the formula:
t = √(d² - r²)
t = √(30² - 24²)
t = √(900 - 576)
t = √324 t = 18
The tangent length is 18 units.
Explanation
The tangent length is determined through the formula by taking the square root of the difference between the distance squared and the radius squared.
Problem 5
A point is 20 units away from the center of a circle with a radius of 16 units. How long is the tangent?
Use the formula:
t = √(d² - r²)
t = √(20² - 16²)
t = √(400 - 256)
t = √144 t = 12
The tangent length is 12 units.
Explanation
By applying the formula, the tangent length is found by subtracting the square of the radius from the square of the distance and taking the square root.
FAQs on Using the Tangent of a Circle Calculator
1.How do you calculate the tangent length?
2.Can the distance be less than the radius?
3.What happens if the distance equals the radius?
4.How do I use a tangent of a circle calculator?
5.Is the tangent of a circle calculator accurate?
Glossary of Terms for the Tangent of a Circle Calculator
- Tangent of a Circle: A straight line that touches a circle at exactly one point without crossing it.
- Radius: The distance from the center of the circle to any point on its perimeter.
- Pythagorean Theorem: A mathematical principle used to calculate the lengths of sides in a right triangle.
- Perpendicular: A line meeting another at a right angle (90 degrees).
- External Point: A point located outside the circle, from which the tangent is drawn.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
