Question

filipe was playing with a triangle on a coordinate plane. the triangles 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? choose 1 answer: a 44% b 48% c 52% d 56%

Explanation:

Step1: Calculate the radius of the circle

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ to find the radius $r$ of the circle. The center of the circle is $(1.2,1.6)$ and a point on the circle is $(0,0)$. So $r=\sqrt{(1.2 - 0)^2+(1.6 - 0)^2}=\sqrt{1.44 + 2.56}=\sqrt{4}=2$.

Step2: Calculate the area of the circle

The area formula of a circle is $A=\pi r^{2}$. Substitute $r = 2$ into the formula, we get $A=\pi\times2^{2}=4\pi\approx4\times3.14 = 12.56$.

Step3: Calculate the percentage

The area of the triangle is 24 square - units. The percentage that the circle covers of the triangle is $\frac{12.56}{24}\times100\%\approx52.33\%\approx52\%$.

Answer:

C. 52%