Part 1 - Application A semi-circle window can be used above a doorway or as an accent window in a room to allow more light in large rooms. The semi-circle window in your home theater room lets too much light in so that the movie experience is not optimal at any time of the day. You research and find there are "room darkening" blinds and shades for semi-circle windows. You can't quite reach the semi-circle window to measure but you are able to measure the window beneath. The height of the rectangle window below is 85 in and the width of the window below the semi-circle is 50 in. What is the area of the semi-circle window so that you can start your search for the correct size? Be sure to show and explain your work.Part 2 - Find the error(s) and solve the problem correctly. Find the equation of the circle. What is the center and radius of the circle? Be sure to show all work and explain your answer. 2 2 X + V + 8x - 2y - 13 = 0 2 2 - X + 8x + y 2y = 13 2 2 - 2y - 1 = 13 + 8 - 1 X + 8x +8 + y 2 (x + 4) 2 + (y - 1 ) = 20 Center (-4, 1) r = 20Part 3 - Discussion Question A student claims that when you double the radius of a sector while keeping the measure of the central angle constant, then you double the area of the sector. Do you agree or disagree? Be sure to show and explain your answer using mathematical language