Question 5 - 20 marks Throughout this question, take care to explain your reasoning carefully. You should round your answers, where necessary, to two significant figures. Aoife is advising a conference company on social distancing measures. The government rules say that people from different households must keep 2 m apart. (a) From an overhead point of view, Aoife models each person as a circle of diameter 0.6 m. Each person is required to have a 'ring' of I'm of free space around them, which is measured from the edge of the circle that represents the person themselves. (i) From an overhead point of view, find the distance from the central point of a person to the edge of the ring of free space around them. [1] (ii) Find the total area of the space occupied by a person and their ring of free space. [1] (b) Aoife then looks at the problem of maintaining social distancing of people seated in an auditorium. Chairs are fixed to the floor and laid out in a rectangular grid arrangement, with each chair aligned exactly with the corresponding chair in front. Each chair is 0.55m wide, and there are no gaps between the chairs. There is a distance of 0.8 m from the back of one chair to the back of the chair in front. Aoife is tasked with solving the problem of finding which chairs can be occupied in the auditorium whilst maintaining a 2m distance between their heads. (i) Let points A and B be the centre points of the backs of adjacent chairs in the same row. Let the point C be the centre point of the chair directly in front of B. What is the distance between points A and O? Can people from different households occupy these two spaces under the 2 m separation rule? [2] (ii) Find all the internal angles of the triangle ABC. [21 (c) Aoife makes a scale drawing of the seating area in the auditorium. (i) In the drawing the length corresponding to BC is 4 cm. What is the reduction scale factor? [1] (ii) Is the angle corresponding to ZBAC on the scale drawing greater than, less than, or the same as ZBAC? Explain your answer. [1] (d) In a breakout spare Anife considers positioning chairs in a different arrangement. She models the positions of these chairs as the points D. E and F. With all lengths measured in metres, DE - 2.8, DF - 4.1 and ZEDF - 25. (i) Find the length EF. Can people from different households be seated in positions E and F according to the 2m rule? 141 (ii) Find the obtuse ZDEF. [4] (iii) Find the area of triangle DEF