Omi67

The number of inches in the perimeter of an equilateral triangle equals the number of square inches in the area of its circumscribed circle. What is the radius, in inches, of the circle? Express your answer in terms of pi and simplest radical form.

A square sheet of paper has area 6 cm^2. The front is white and the back is black. When the sheet is folded so that point A rests on the diagonal as shown, the visible black area is equal to the visible white area. How many centimeters is A from its original position? Express your answer in simplest radical form.

A circle is drawn that intersects all three sides of triangle PQR  as shown below. Prove that if AB=CD=EF, then the center of the circle is the incenter of triangle PQR.In your proof please explain with atleast one paragraph.

What is the perimeter of pentagon  ?

In triangle A, B, C, AB=13, AC=15 and BC=14. Let I be the incenter. The incircle of triangle ABC touches sides BC, AC, and AB at D, E, and F, respectively. Find the length of BI.

In triangle ABC, AB = 17, AC = 8, and BC = 15. Let D be the foot of the altitude from C to AB. Find the area of triangle ACD. 

If f(x)=x3, what is the value of f-1(8)/(f(8))-1?

4. The graph of $y=f(x)$ is shown below in red. Given that $f$ is invertible, find $f^{-1}(4)$.

5. What are the coordinates of the points where the graphs of $f(x)=x^3-x^2+x+1$ and $g(x)=x^3+x^2+x-1$ intersect? Give your answer as a list of points separated by semicolons, with the points ordered such that their $x$-coordinates are in increasing order. (So "(1,-3); (2,3); (5,-7)" - without the quotes - is a valid answer format.)

1. The graph of $y=f(x)$ is shown in red below. For how many values of $c$ is $f(c) = -1$?

     4 values