Question

Hey GT or anybody, can you help me with this? I stuck on it.

Q: A circle is inscribed in a square whose vertices have coordinates R(0, 4), S(6, 2), T(4, -4), and U(-2, -2). Find the equation of the circle.

Answer 1

center of the circle will be the midpoint of the corners.
\[(\frac{-2+6}{2},\frac{-2+2}{2})\]
\[(2,0)\] if my picture is right

Answer 2

hard part if finding the radius of the circle, which requires finding the distance from the center of the circle to one of the line segments joining the points.

Answer 3

or you can find the length of any line segment, and take half of that for the radius

Answer 4

SU and RT are diagonals. Mid point of both those segments should yield the coordinates of the center of the circle. You then need radius of the circle, which will be the same as half the side of the square (you can pick any one of the four sides and use distance formula). Once you have all that, equation of the circle can be constructed.

Answer 5

for example from
\[(0,4)\] to
\[(6,2)\] the square of the distance is
\[6^2+2^2=40\]
making the distance
\[2\sqrt{10}\]
half of that is
\[\sqrt{10}\]so i suppose your equation is
\[(x-2)^2+y^2=10\]

Answer 6

what gt said!

Answer 7

Correct!

Answer 8

Satellite, Nice formatting!