Mathematics 2000 JAMB Past Questions - Question 27: An equilateral triangle of side 3 is inscribed in a circle .Find the radius of the circle.

Correct Answer

C

Explanation

check solution in the diagram aboveTo find the radius of the circle inscribed in an equilateral triangle of side length 3, we can use the properties of an equilateral triangle and the relationship between the radius of the inscribed circle and the side length of the triangle.In an equilateral triangle, all sides are equal, and each angle measures 60 degrees. The radius of the inscribed circle is perpendicular to each side of the triangle and bisects it.Let's draw the radius from the center of the circle to one of the vertices of the equilateral triangle. This radius divides the equilateral triangle into two congruent right triangles.The hypotenuse of each right triangle is the side length of the equilateral triangle, which is 3. The base of each right triangle is half the side length of the equilateral triangle, which is 3/2.Using the Pythagorean theorem, we can find the height of each right triangle, which is also the radius of the inscribed circle:(radius)^2 + (3/2)^2 = 3^2(radius)^2 + 9/4 = 9(radius)^2 = 9 - 9/4(radius)^2 = 36/4 - 9/4(radius)^2 = 27/4radius = √(27/4)radius = √27 / √4radius = (3√3) / 2Therefore, the radius of the circle inscribed in the equilateral triangle of side length 3 is (3√3) / 2. maths 2000 31.jpgAn equilateral triangle of side 3 is inscribed in a circle .Find the radius of the circle.