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Circumradius of Equilateral Triangle Formula:
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The Circumradius of Equilateral Triangle is the radius of a circumcircle touching each of the Equilateral Triangle's vertices. It is a fundamental geometric property that describes the size of the circle that passes through all three vertices of the triangle.
The calculator uses the formula:
Where:
Explanation: In an equilateral triangle, the circumradius is exactly twice the inradius. This relationship holds true for all equilateral triangles regardless of their size.
Details: Calculating the circumradius is important in various geometric applications, including triangle construction, circle packing problems, and in engineering designs where circular components interact with triangular structures.
Tips: Enter the inradius value in meters. The value must be positive and greater than zero. The calculator will automatically compute the corresponding circumradius.
Q1: Why is the circumradius exactly twice the inradius in an equilateral triangle?
A: This is a unique geometric property of equilateral triangles where the centroid, circumcenter, and incenter all coincide, creating this specific 2:1 ratio between circumradius and inradius.
Q2: Can this formula be used for other types of triangles?
A: No, this specific relationship (r_c = 2 × r_i) only applies to equilateral triangles. Other triangle types have different relationships between circumradius and inradius.
Q3: What are the units for circumradius and inradius?
A: Both are measured in length units (meters, centimeters, inches, etc.). The units must be consistent between input and output.
Q4: How accurate is this calculation?
A: The calculation is mathematically exact for perfect equilateral triangles. The accuracy depends on the precision of the input value.
Q5: What if I have the side length instead of the inradius?
A: You would need to first calculate the inradius using the formula r_i = (s × √3)/6, where s is the side length, then use this calculator.