MT1100 Problem Sheet 3 Due: Thursday 22nd October 2020 at 10:00. Please write your name clearly at the top of each page. Scan your work as a single-file PDF. Do not use too high a resolution to ensure the file size remains below 20 MB (the upper limit is 50MB). Then upload your PDF file onto Moodle, as per the instructions available from the General Information box on Moodle. You are encouraged to leave your handwritten comments to the marker on the first or last page of your homework submission. 1. Let C1 be the circle with centre (0, 0) and radius 2. Let C2 be the circle with centre (1, 2) and radius 3. Find the points of intersection of the circles C1 and C2. 2. Let A and B be distinct points. In the diagram below, ABDC is a rectangle (which can be any height you choose), G bisects AB, and EF is the perpendicular to AB dropped from E. C D 0 E A F G B (i) Write down a list of ruler and compass steps (you can quote constructions from the lectures for some steps) to show that F can be constructed from A and B using a ruler and compass. (ii) Show that |AF| = |AB|/3. Hint: As a first step, note that the triangles AEF and ADB are similar. Then find another pair of similar triangles. [The diagram, together with the list of steps in (i) and the justification in (ii) shows that trisecting a length using a ruler and compass is possible.]