SOLUTION: A circle is inscribed in a square with vertices(-9,-3),(-1,-3),(-9,5) and (-1,5). A)find the coordinates of the center of the circle B)find the area of the circle C) find the r

Algebra ->  Points-lines-and-rays -> SOLUTION: A circle is inscribed in a square with vertices(-9,-3),(-1,-3),(-9,5) and (-1,5). A)find the coordinates of the center of the circle B)find the area of the circle C) find the r      Log On


   

Question 889557: A circle is inscribed in a square with vertices(-9,-3),(-1,-3),(-9,5) and (-1,5).
A)find the coordinates of the center of the circle
B)find the area of the circle
C) find the radius of a circle circumscribed about the square
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
More than one way to do this. Look for the midpoint of any pair of opposite corners. Use distance formula to find half the length of a diagonal.

A pair of opposite corners is (-1,-3) and (-9,5).

Center point should be at x=%28-1-9%29%2F2=-4 and y=%28-3%2B5%29%2F2=1

Diagonal length, sqrt%28%28-1-%28-9%29%29%5E2%2B%28-3-5%29%5E2%29
sqrt%28%288%29%5E2%2B%28-8%29%5E2%29
sqrt%28128%29
sqrt%2864%2A2%29
8%2Asqrt%282%29
HALF of that is highlight_green%284%2Asqrt%282%29%29. This is also the size of the radius of the circle.

Equation for the circle is highlight%28%28x%2B4%29%5E2%2B%28x-1%29%5E2=%284sqrt%282%29%29%5E2%29.