Question

Find the largest area of an isosceles triangle inscribed in a circle of radius 3

Answer 1

The largest area of an isosceles triangle inscribed in a circle with a radius of 3 units is approximately 5.8095 square units.

Step-by-step explanation:

The largest area of an isosceles triangle inscribed in a circle can be found by maximizing the base of the triangle. In this case, the base of the isosceles triangle is equal to the diameter of the circle, which is 6 (2 times the radius). The height of the triangle can be found using Pythagorean theorem, where the hypotenuse is the radius of the circle and the legs are half of the base. So, the height is sqrt(3^2 - 1.5^2) = sqrt(3.75) = 1.9365. Therefore, the largest area of the isosceles triangle is (1/2) * 6 * 1.9365 = 5.8095 square units.

Answer 2

Here is the answer and explanation all together