Try this beautiful problem from Geometry based on Circumscribed Circle
The number of inches in the perimeter of an equilateral triangle equals the number of square inches in the area of its circumscribed circle. What is the radius, in inches, of the circle?
Geometry
Triangle
Circle
Answer: \(\frac{3\sqrt3}{\pi}\)
AMC-10A (2003) Problem 17
Pre College Mathematics
Let ABC is a equilateral triangle which is inscribed in a circle. with center \(O\). and also given that perimeter of an equilateral triangle equals the number of square inches in the area of its circumscribed circle.so for find out the peremeter of Triangle we assume that the side length of the triangle be \(x\) and the radius of the circle be \(r\). then the side of an inscribed equilateral triangle is \(r\sqrt{3}\)=\(x\)
Can you now finish the problem ..........
The perimeter of the triangle is=\(3x\)=\(3r\sqrt{3}\) and Area of the circle=\(\pi r^2\)
Now The perimeter of the triangle=The Area of the circle
Therefore , \(3x\)=\(3r\sqrt{3}\)=\(\pi r^2\)
can you finish the problem........
Now \(3x\)=\(3r\sqrt{3}\)=\(\pi r^2\) \(\Rightarrow {\pi r}=3\sqrt 3\) \(\Rightarrow r=\frac{3\sqrt3}{\pi}\)
AMC - AIME Boot Camp... for brilliant students.
Use our exclusive one-on-one plus group class system to prepare for Math Olympiad
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.