an equilateral triangle of side 10cm is inscribed in a circle. find the radius of the circle? show the solution

Question

Nky · Accepted Answer

If an equilateral triangular prism of side 10cm is inscribed in a circle. Find the radius of the circle

oobleck · Answer

each inscribed angle is 60°
That means the central angle subtending one side is 120°
The altitude from the center of the circle to a side forms 30-60-90 triangles, with hypotenuse equal to the radius.
Now use what you know about the sides of such triangles to find the radius

Pat · Answer

Actually this problem is not hard.Trigonometrical ratios can be used well like for example sign rule, ie let the radius of the circle be r.taking the distance from the two corners of the triangle where they are in contact with the circumference.The two will intersect each other at a point inside the triangle call it O.You will realize that the intersection of two sides form an angle 120°.Using the sine rule then the r/sin30° =10/sin120°
R=5.77cm