Circle Geometry: Verify that Diameter = 2 × Radius

Circle Properties with Diameter-Radius Relationships

The diameter of a circle is twice as long as its radius.

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

The diameter of a circle is twice as long as its radius.

2

Step-by-step solution

The diameter of a circle is defined as the distance across the circle through its center. It is directly related to the radius, which is the distance from the center to a point on the circumference of the circle.

By the standard definition in geometry, the diameter (d d ) of a circle is expressed in terms of its radius (r r ) as:

d=2r d = 2r

This equation clearly states that the diameter is twice the length of the radius. Hence, the statement, “The diameter of a circle is twice as long as its radius,” aligns with this fundamental geometric property.

Therefore, the statement is True.

3

Final Answer

True

Key Points to Remember

Essential concepts to master this topic
  • Definition: Diameter is the distance across circle through center
  • Formula: d=2r d = 2r where d is diameter, r is radius
  • Verification: Draw any circle and measure: diameter always equals 2 × radius ✓

Common Mistakes

Avoid these frequent errors
  • Confusing diameter and radius measurements
    Don't mix up which measurement is which = wrong calculations! Students often think radius is the full distance across or that diameter is half the distance. Always remember: radius goes from center to edge, diameter goes all the way across through the center.

Practice Quiz

Test your knowledge with interactive questions

M is the center of the circle.

Perhaps \( MF=MC \)

MMMAAABBBCCCDDDEEEFFFGGGHHH

FAQ

Everything you need to know about this question

What's the difference between radius and diameter?

+

The radius goes from the center to any point on the circle's edge. The diameter goes all the way across the circle, passing through the center. Think of it like this: radius is half-way, diameter is all-the-way!

Why is diameter always exactly twice the radius?

+

Because the diameter passes through the center! It's like putting two radius lines end-to-end. Since each radius has the same length from center to edge, diameter = radius + radius = 2 × radius.

Does this rule work for all circles?

+

Yes, always! Whether your circle is tiny like a coin or huge like a ferris wheel, d=2r d = 2r is a universal rule that never changes.

How can I remember this relationship?

+

Try this: "Diameter divides in two" - the diameter can be split into two equal radius pieces. Or think: "Radius is half, diameter is all!"

What if I'm given the diameter and need the radius?

+

Just reverse the formula! If d=2r d = 2r , then r=d2 r = \frac{d}{2} . So radius equals diameter divided by 2.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Circle questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations