Question: What is the circumradius R of a triangle with sides a, b, c?
Options:
abc/4A
A/(abc)
2A/(a+b+c)
a+b+c/2
Correct Answer: abc/4A
Solution:
The circumradius R of a triangle is given by the formula R = abc/(4A), where A is the area of the triangle.
What is the circumradius R of a triangle with sides a, b, c?
Practice Questions
Q1
What is the circumradius R of a triangle with sides a, b, c?
abc/4A
A/(abc)
2A/(a+b+c)
a+b+c/2
Questions & Step-by-Step Solutions
What is the circumradius R of a triangle with sides a, b, c?
Step 1: Understand that the circumradius R is the radius of the circle that can be drawn around the triangle.
Step 2: Know that the formula to find the circumradius R is R = abc / (4A).
Step 3: Identify the sides of the triangle as a, b, and c.
Step 4: Calculate the area A of the triangle using a suitable method (like Heron's formula or base-height method).
Step 5: Substitute the values of a, b, c, and A into the formula R = abc / (4A).
Step 6: Perform the calculations to find the value of R.
Circumradius of a Triangle – The circumradius R is the radius of the circumcircle that passes through all three vertices of the triangle, calculated using the sides and area of the triangle.
Area of a Triangle – The area A can be calculated using various methods (e.g., Heron's formula, base-height formula), which is essential for applying the circumradius formula.
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