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Given a square ABCD, use Euclid's system to show that there is an equilateral triangle DEF with the same area as square ABCD.
A. Given a square ABCD, use Euclid’s system to show that there is an equilateral triangle △DEF with the same area as square ABCD.B. Suppose the radius of the incircle of △ABC is r and the semiperimeter of the triangle is s = 1 (|AB| + |BC| + |CA|). Show that the area of the triangle is equal to rs.C. Suppose ABCD is a cyclic quadrilateral, i.e. A, B, C, and D are points on a circle, given in order going around the circle. Show that if we join each of A, B, C, and D to the orthocentre of the triangle formed by the other three, then the resulting line segments all intersect in a common midpoint M.D.Suppose that the incircle of △ABC is tangent to the sides BC, AC, and AB at the points P, Q, and R, respectively. Show that AP, BQ, and CR are concurrent.D.
