Question

Filipe was playing with a triangle on a coordinate plane. The triangle's area is 24 square units. The largest circle he can fit in the triangle is centered at (0,0) and passes through the point (1.2,1.6) Approximately what percentage of the triangle does the circle cover?

Answer 1

52.36%

Explanation:

First, you need to find the radius of the circle. You can do this by using the Pythagorean theorem, which states a^2+b^2=c^2. In this case, a and b are equal to 1.2 and 1.6, and c is the radius of the circle. Plugging in we get 1.2^2+1.6^2=c^2 or 1.44+2.56=c^2 or 4=c^2. Finding the square root of both sides of the equation, we find that 2=c. Now that we have the radius, we can find the area of the circle. The area of a circle is expressed as πr^2, and plugging in 2 for r we get an area of 4π, or ~12.56637. Now all we do is divide 12,56637 by 24 and get what percentage of the area of the triangle the circle covers, which is roughly 0.5236, or 52.36%