Grissom High School Math Tournament Geometry March 15, 2003

Transcription

1 . Simplify: rissom High School Math Tournament eometry March 5, ind the absolute value of the difference between the degree measures of the supplement and the complement of an angle with degree measure If x is the geometric mean of 2 and 8, find 2x 4.. 7/4. 5/4. 4. /2. /4 4. ind the area of a triangle given that = 5 4, = 8 2 and m = The diagram on the right shows a right triangle bordered by squares. If = 4 and = 40, find the area of the shaded region ind the total surface area of a cylinder if the base area is 49 and the height is triangle has sides 2, 8, and x, and x is an integer. Let be the smallest possible value for x and be the largest possible value for x. ind What is the sum of the degree measures of the exterior angles in a convex dodecagon? ind the area of a quadrilateral with vertices are located at points (0,0), (,0), (0,4), and (,8)

2 0. is a diameter of the circle and is a chord whose length is equal to the length of the radius of the circle. ind the degree measure of arc Let be the sum of the areas of a chiliagon and a pentagon. The area of the chiliagon is three times that of the pentagon. Let be the sum of two-thirds the area of the pentagon and one-third the area of the chiliagon. ind the ratio of to.. /8. 7/7. 5/2. 4/9. /2 2. regular hexagon has an area of 45. What is its perimeter? n equilateral triangle is inscribed in a circle, and the circle is inscribed in another equilateral triangle. ind the ratio of the area of the smaller triangle to that of the larger triangle.. :4. 2:7. :. :2. 2: 4. The diagram below shows a rectangle and a circle with the center of the circle below the rectangle, one side of the rectangle tangent to the circle, and two vertices of the rectangle on the circle. The longest side of the rectangle is 6, and the radius of the circle is 0. ind the area of the rectangle oints and Q are diagonally opposite vertices of a cube whose side has length s. Let be the shortest path from to Q. Let be the shortest path an ant can take in crawling from to Q on the surface of a cube. ind -. ( 2). s. ( 5 ) s. s. 2s. ( 2 5 ) s 6. ircles and intersect at points and, and is a square. ind the area of the region common to both circles if =

3 7. iven: ==, =6, =9, = ind:.. /2. 9/2. /2. 5/2. 2/2 8. In quadrilateral, diagonals and are perpendicular and is perpendicular to H. iven m H=67, find m H 9. dog is tied with a leash of length 6 to midpoint of a side of the parallelogram fence. = 6 and = 2. The dog has to stay outside of the fenced yard. cat is sitting outside the fenced yard within 2 feet of the intersection of the diagonals of the yard. ind the probability that the dog on the leash can catch the cat.. 5/88. 5/28. /6. 5/22. 5/ ind the radius of a sphere inscribed in a regular tetrahedron which has a height of 8.. ¼. ½ /2 2. In rectangle, =42, =9. In parallelogram, has half the length of. ind the area of the shaded region ircle is inscribed in a semicircle so that the diameter of circle is the radius of the semicircle. ircle is externally tangent to circle, and circle is tangent to both the arc and the diameter of the semicircle. If the length of the radius of the circle is, find the area inside the semicircle but outside of the 2 circles

4 2. The sum of the areas of circle O and circle, which are tangent to each other, is 28 and O is 6. ind the length of external tangent O 24. In quadrilateral, diagonals and intersect at.,,, H are the centroids of triangles,,, and, respectively. If the area of quadrilateral is 8, find the area of the quadrilateral H. The centroid of a triangle is the point of intersection of the medians of the triangle If and 4, find T. In circle, the radius is 2. If the area of the shaded region is expressed in simplest form as a b c, find a b c. 60 T2. In the circle, is a diameter. ind m if =4, =2, and = T. iven Q x y 6x 6y 7 x y 4x 0y 29, find the minimum value of Q. y (x,y) (8,) x (2, -5)

5 OMTRY NSWRS: T. 57 T 2. 5 T. 0