Question

what is the perimeter triangle inscribed in a circle if the radius of a circle is 12unit​

Answer 1

Answer:

perimeter or triangle = 48√2 units

Answer 2

hi dear

your answer is

72.89 units. Check: circumference of the circle is 75.4, so the answer is “reasonable.”

Think of a heptagon as 7 isosceles triangles with side lengths equal to the radius of the circle. The bases of these form the perimeter of the heptagon. So we need to find the length of one base. These triangles can be divided equally into right triangles, and simple trigonometry gives us the answer.

Angle opposite right triangle base is 25.71 deg (360/14), length of base is (b/12 = sin(25.71)) = 5.21. Double that to get base length of the isosceles triangle, and multiply by 7 to get perimeter of heptagon.

EDIT: Thanks to David Shaffer for catching my erroneous use of “equilateral.” He is correct of course that these are isosceles triangles (at least two sides have the same length), not equilateral (where all three side must be the same length)

hopes its helps you