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Assignment help 2895

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.

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