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Hagerty Invitational Geometry Team: Question #1 Let be the area of a circle with radius . Let be the perimeter of a circle with radius . Let be the length of the longest chord that can be drawn in a circle with radius . Let be the area of a semicircle with radius . Find . Hagerty Invitational Geometry Team: Question #2 For the following questions, refer to a regular hexagon with sides of length 4. Let be the length of the longest diagonal in the hexagon. Let be the maximum number of diagonals that can be drawn in the hexagon. Let be perpendicular distance between two opposite sides. Let be the area of the hexagon. Find . Hagerty Invitational Geometry Team: Question #3 Find the sum of the first 8 terms in the geometric sequence with first term 2 and common ratio 3. Hagerty Invitational Geometry Team: Question #4 In star GEOISBALRZ to the right, Let be the measure in degrees of . Let be the measure in degrees of EIB. Let be the measure in degrees of Let be the measure in degrees of Let be the measure in degrees of . Let be the measure in degrees of Find . Hagerty Invitational How many diagonals does a convex 2011-gon have? Hagerty Invitational In the diagram with angles of measure and , Z Geometry Team: Question #5 , find Geometry Team: Question #6 . _ Hagerty Invitational + In the diagram to the right, Let be the ratio of lengths Let be the ratio of areas of Geometry Team: Question #7 to . to Express the ratios as a fraction. Find . . Hagerty Invitational How many of the following statements are true? Geometry Team: Question #8 All pairs of lines that do not intersect are parallel. The geometric mean of and is The diagonal of a cube with edges of length is If the cosine of angle is , the sine of is . A cube can be inscribed in a sphere. Hagerty Invitational Geometry Team: Question #9 Use the following coordinates for this question: A (-5, 3); W (-2, 9); E (4, 8); S (7, 1); U (2, -3); M (-3, -3). Let be the area of the quadrilateral AWEM. Let be the area of the quadrilateral SUME. What is Hagerty Invitational Geometry Team: Question #10 In a 9-12-15 right triangle, what is the sum of the altitudes drawn to each side of the triangle? Hagerty Invitational Geometry Team: Question #11 In rectangle , , , and . What is the area of quadrilateral ? Hagerty Invitational Geometry Team: Question #12 Let be the angle in degrees of , if the complement of is one third of the supplement of . Let be the angle in degrees of , if three times is equal to two times the supplement of . Find . Hagerty Invitational Geometry Team: Question #13 How many distinct permutations of the word MISTRESSSHIP are there? Hagerty Invitational Geometry Team: Question #14 What is the measure in degrees of one exterior angle of a regular 2011-gon? Hagerty Invitational Geometry Team: Question #15 Let be the area of an equilateral triangle with sides of length 3. Let be the hypotenuse of a triangle with legs of length 9 and 40. Let be the volume of a cylinder with radius 3 and height 3. Find