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Problem of the Week: June - August 1996 About the Problem of the Week || All Problems || Search POWs & POMs June 3-7 - How far above the earth?: The radius of the earth (at the equator) is 6374 km. How far from the earth (above the equator) would you have to go into space to get 1/4 of the equator in a picture? 1/3 of the equator? 1/2? June 10-14 - Garfield's Proof: Explain future president James Garfield's proof of the Pythagorean theorem. June 17-21 - Folded paper: A 6-inch by 8-inch piece of paper is folded so that opposite vertices touch. How long is the fold? June 24-28 - Area of triangle ABC: In triangle ABC, AC = 18 and D is the point on AC for which AD = 5. Perpendiculars drawn from D to AB and CB have lengths of 4 and 5 respectively. What is the area of triangle ABC? July 1-5 - What is the value of AB?: In parallelogram ABCD, the bisector of angle <ABC intersects AD at P. If PD=5, BP=6, and CP=6, what is the value of AB? July 8-12 - What's the area of the trapezoid?: One diagonal of a square serves as the shorter base of a trapezoid, and a line through one of the vertices of the square contains the other base. The legs of the trapezoid are extensions of two sides of the square. If the area of the square is 2800, what is the area of the trapezoid? July 15-19 - How long is the triangle's base?: In an isosceles triangle, the perpendicular bisector of one leg passes through the midpoint of the base. If the length of this leg is 10, how long is the base? July 22-26 - Area of the smaller square: One altitude of an equilateral triangle is a side of one square, and one side of the same equilateral triangle is a side of a second square. The area of the larger of these squares is 56; what is the area of the smaller square? July 29-August 2 - Coplanar, nonoverlapping hexagons: Regular hexagon ABCDEF has side AF in common with regular hexagon AFGHIJ and side BC in common with regular hexagon BCKLMN. All three hexagons are coplanar and nonoverlapping. If AB = 64, what is the value of JN? August 5-9 - Distance from point to midpoint: The lengths of the sides of a triangle are 25, 29, and 36. There is a point on the longest side of the triangle whose distance from the opposite vertex is 20. What is the distance from this point to the midpoint of the shortest side? August 12-16 - What's the value of x?: Both legs of an isosceles triangle are radii of a circle, and the length of each radius is 6. The distance from the center of the circle to a point P on the base of the triangle is 4. If the distances from P to the triangle's other vertices are 5 and x, what is the value of x? August 19-23 - Largest possible area of the triangle: Two vertices of an equilateral triangle lie on a diameter of a circle whose area is 36pi, and the third vertex lies on the circle. What is the largest possible area of the triangle? August 26-30 - Trapezoid base midpoints: In a trapezoid, the lengths of the bases are 4 and 16, and the lower base angles are 30 degrees and 60 degrees. What is the distance between the midpoints of the two bases? On to September 1996 || Back to Jan.-May 1996 || Back to 1995 [Privacy Policy] [Terms of Use] Home || The Math Library || Quick Reference || Search || Help  © 1994-2008 Drexel University. All rights reserved. http://mathforum.org/ The Math Forum is a research and educational enterprise of the Drexel School of Education.