Question: What is the circumradius of an equilateral triangle with side length a?
Options:
a/√3
a/2
a/√2
a/√3
Correct Answer: a/√3
Solution:
The circumradius R of an equilateral triangle is given by R = a/(√3).
What is the circumradius of an equilateral triangle with side length a?
Practice Questions
Q1
What is the circumradius of an equilateral triangle with side length a?
a/√3
a/2
a/√2
a/√3
Questions & Step-by-Step Solutions
What is the circumradius of an equilateral triangle with side length a?
Step 1: Understand that the circumradius is the radius of the circle that can be drawn around the triangle, touching all its vertices.
Step 2: Know that for an equilateral triangle, all sides are equal and all angles are 60 degrees.
Step 3: Use the formula for the circumradius R of an equilateral triangle, which is R = a / (√3).
Step 4: Substitute the side length 'a' into the formula to find the circumradius.
Circumradius of a Triangle – The circumradius is the radius of the circumcircle, which is the circle that passes through all the vertices of the triangle.
Properties of Equilateral Triangles – In an equilateral triangle, all sides and angles are equal, which simplifies the calculation of the circumradius.
Formula Derivation – Understanding how to derive the circumradius formula for different types of triangles, particularly equilateral ones.
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