For A Circle With Centre O And Radius 5 Cm, Which Of The Following Statements Is True? P: Distance Between Every Pair Of Parallel Tangents Is 5 Cm Q: Distance Between Every Pair Of Parallel Tangents Is 10 Cm. R: Distance Between Every Pair Of Parallel
Introduction
In geometry, a circle is a set of points that are all equidistant from a central point called the centre. The distance from the centre to any point on the circle is called the radius. In this article, we will explore the properties of a circle with centre O and radius 5 cm, and determine which of the given statements is true.
Understanding the Properties of a Circle
A circle is a closed shape with no beginning or end. It is a set of points that are all equidistant from a central point called the centre. The distance from the centre to any point on the circle is called the radius. The radius is the longest distance from the centre to any point on the circle.
Key Properties of a Circle:
- A circle is a closed shape with no beginning or end.
- All points on the circle are equidistant from the centre.
- The distance from the centre to any point on the circle is called the radius.
- The radius is the longest distance from the centre to any point on the circle.
Understanding Parallel Tangents
Parallel tangents are lines that touch the circle at two points and are parallel to each other. The distance between two parallel tangents is called the distance between the tangents.
Key Properties of Parallel Tangents:
- Parallel tangents are lines that touch the circle at two points.
- Parallel tangents are parallel to each other.
- The distance between two parallel tangents is called the distance between the tangents.
Understanding the Distance Between Parallel Tangents
The distance between two parallel tangents is equal to the diameter of the circle. The diameter is twice the radius of the circle.
Key Properties of the Distance Between Parallel Tangents:
- The distance between two parallel tangents is equal to the diameter of the circle.
- The diameter is twice the radius of the circle.
Applying the Properties to the Given Statements
Now that we have understood the properties of a circle and parallel tangents, let's apply them to the given statements.
Statement P: Distance between every pair of parallel tangents is 5 cm
This statement is incorrect because the distance between two parallel tangents is equal to the diameter of the circle, which is twice the radius. In this case, the radius is 5 cm, so the diameter is 10 cm.
Statement Q: Distance between every pair of parallel tangents is 10 cm
This statement is correct because the distance between two parallel tangents is equal to the diameter of the circle, which is twice the radius. In this case, the radius is 5 cm, so the diameter is 10 cm.
Statement R: Distance between every pair of parallel tangents is 10 cm
This statement is the same as statement Q, and is therefore also correct.
Conclusion
In conclusion, the correct statement is Q: Distance between every pair of parallel tangents is 10 cm. This is because the distance between two parallel tangents is equal to the diameter of the circle, which is twice the radius. In this case, the radius is 5 cm, so the diameter is 10 cm.
Frequently Asked Questions
Q: What is the distance between two parallel tangents?
A: The distance between two parallel tangents is equal to the diameter of the circle.
Q: What is the diameter of a circle?
A: The diameter of a circle is twice the radius of the circle.
Q: What is the radius of a circle?
A: The radius of a circle is the distance from the centre to any point on the circle.
References
Further Reading
Related Articles
- For a Circle with Centre O and Radius 5 cm, Which of the Following Statements is True?
- Understanding the Properties of a Circle
- Understanding Parallel Tangents
- Understanding the Distance Between Parallel Tangents
- Applying the Properties to the Given Statements
- Conclusion
- Frequently Asked Questions
- References
- Further Reading
- Related Articles
Introduction
In our previous article, we explored the properties of a circle with centre O and radius 5 cm, and determined which of the given statements is true. In this article, we will answer some frequently asked questions (FAQs) related to the properties of a circle and parallel tangents.
Q&A
Q: What is the distance between two parallel tangents?
A: The distance between two parallel tangents is equal to the diameter of the circle.
Q: What is the diameter of a circle?
A: The diameter of a circle is twice the radius of the circle.
Q: What is the radius of a circle?
A: The radius of a circle is the distance from the centre to any point on the circle.
Q: How do you find the distance between two parallel tangents?
A: To find the distance between two parallel tangents, you need to find the diameter of the circle. The diameter is twice the radius of the circle.
Q: What is the relationship between the radius and the diameter of a circle?
A: The diameter of a circle is twice the radius of the circle.
Q: What is the relationship between the distance between two parallel tangents and the radius of a circle?
A: The distance between two parallel tangents is equal to the diameter of the circle, which is twice the radius of the circle.
Q: Can you give an example of a circle with centre O and radius 5 cm?
A: Yes, a circle with centre O and radius 5 cm is a circle with a centre at point O and a radius of 5 cm.
Q: What is the distance between two parallel tangents in a circle with centre O and radius 5 cm?
A: The distance between two parallel tangents in a circle with centre O and radius 5 cm is 10 cm.
Q: Why is the distance between two parallel tangents equal to the diameter of the circle?
A: The distance between two parallel tangents is equal to the diameter of the circle because the diameter is the longest distance across the circle, and the distance between two parallel tangents is the longest distance between two points on the circle.
Q: Can you give a real-life example of a circle with centre O and radius 5 cm?
A: Yes, a real-life example of a circle with centre O and radius 5 cm is a coin with a diameter of 10 cm.
Conclusion
In conclusion, we have answered some frequently asked questions (FAQs) related to the properties of a circle and parallel tangents. We hope that this article has provided you with a better understanding of the properties of a circle and parallel tangents.
Frequently Asked Questions (FAQs) Related to the Properties of a Circle and Parallel Tangents
- What is the distance between two parallel tangents?
- What is the diameter of a circle?
- What is the radius of a circle?
- How do you find the distance between two parallel tangents?
- What is the relationship between the radius and the diameter of a circle?
- What is the relationship between the distance between two parallel tangents and the radius of a circle?
- Can you give an example of a circle with centre O and radius 5 cm?
- What is the distance between two parallel tangents in a circle with centre O and radius 5 cm?
- Why is the distance between two parallel tangents equal to the diameter of the circle?
- Can you give a real-life example of a circle with centre O and radius 5 cm?
References
Further Reading
Related Articles
- For a Circle with Centre O and Radius 5 cm, Which of the Following Statements is True?
- Understanding the Properties of a Circle
- Understanding Parallel Tangents
- Understanding the Distance Between Parallel Tangents
- Applying the Properties to the Given Statements
- Conclusion
- Frequently Asked Questions
- References
- Further Reading
- Related Articles