Need help with this asap pls!!

Question

Create a round object to hang in your window that will touch the midpoints of all four edges of your window (think about what shape your window must be so that a circular object will touch the midpoints of all four edges). Draw the window and label its vertices, then draw the circular object within the window so that it touches the midpoints of all four edges of your window. List the midpoints of all four edges of your window. Determine the center and radius of your circle. Be creative!

Draw your window on a graph, using a shape that will allow your circular object to touch the midpoints of all four edges of the window. Do not center your window on the graph. Label the vertices of the window, then draw your circular object within the window so that it touches the midpoints of all four edges of the window.

Determine the center of your circle and use the midpoint formula to verify it. You must show all work.

Determine the radius of your circle and use the distance formula to verify it. You must show all work.

Answer 1

(x-h)^2 + (y-k)^2 = r^2

center is (h,k)

radius = r

top of the circle is (h,r+k) = midpoint of the window's top

circle's bottom is (h,k-r)=midpoint of the window bottom

left edge of the circle is (h-r, k)=midpoint of the window's left side

right edge of the circle is (h+r, k)= midpoint of the window's right side

the window square is 2r by 2r. its vertices are (h-r, r+k), (h+r, r+k), (h-r, r-k), (h+r, r-k)

midpoint of the square's bottom is (h-r, r-k) and (h+r, r-k)

= average of the coordinates =((h-r+h+r)/2, (r-k+r-k)/2)

= (h, r-k) = bottom edge of the circle

simplest circle and square would be both centered at (0,0) with circle radius = 1 and squares' vertices (-1,1),(1,1), (-1,-1) and (1,-1)

with circle's top edge = (0,1), bottom edge (0,-1), left edge = (-1,0) and right edge = (1,0)

top edge = (0,1) which is the midpoint of (-1,1) and (1,1)

average the x coordinates = 0

average of the y coordinates = 1

midpoint of top of the square is the same point as the top edge of the circle.

(h-r, r)