Geometry Assignment 2627865

A symbol is made with a circle which is inscribed by one equilateral triangle and circumscribed by another. The difference in areas between the two triangles is 25 cm2 . What is the radius of the circle? [7 marks] Question 2 The points M, N and P respectively lie on the sides AB, BC and CA of triangle ABC. Using Cabri Geometry, show that circles BMN, CNP and AMP have a common point. Prove that this point is common. [Hint: draw only two circles for proof] [8 marks] Question 3 Two mutually perpendicular chords of a circle, AB and CD, meet at P. If M is the midpoint of BC, prove that MP produced is perpendicular to AD. [Hint: Show MP = MC first] [9 marks] Question 4 A,B,C and D are Document Preview:

Australian Catholic University Melbourne Campus Semester 1 Geometry MATH205 thAssignment Part 1 Due: Monday March 19 2018 • Please attach an assignment cover sheet. • This must be your own unaided work: see the unit outline for the Regulations. • Show all working. Question 1 A symbol is made with a circle which is inscribed by one equilateral triangle and circumscribed by another. The difference in areas between the two triangles is 25 2cm . What is the radius of the circle? [7 marks] Question 2 The points M, N and P respectively lie on the sides AB, BC and CA of triangle ABC. Using Cabri Geometry, show that circles BMN, CNP and AMP have a common point. Prove that this point is common. [Hint: draw only two circles for proof] [8 marks] Question 3 Two mutually perpendicular chords of a circle, AB and CD, meet at P. If M is the midpoint of BC, prove that MP produced is perpendicular to AD. [Hint: Show MP = MC first] [9 marks] Question 4 A,B,C and D are points on a circle such that AB || CD. Draw this and prove that AD = BC. [8 marks] Question 5 B is a point on the circumference of a circle and AC is a diameter. D is a point on line AB produced and the perpendicular from D to AC meets BC in E and AC in F. (a) Use Cabri Geometry to produce a diagram of this problem. (b) Prove that ABEF is a cyclic quadrilateral and explain why ?AEB = ?AFB and ?DEB = ?BAF. (c) Where is the centre of the circle through A,B,E,F? [2 + 5 + 1 = 8 marks]

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