High School Challenge

Week Ending 10-11-98

Send Answer to: ucfcasio@pegasus.cc.ucf.edu


Congratulations to Dawn Gordon of Louisa County High School in Mineral, VA. Dawn wins the Casio CFX-9850G Color Graphing calculator.


Triangle Medians, Altitudes and Angle Bisectors


1) In any triangle, the sum of the three altitudes is greater than the semi-perimeter of that triangle.
2) In any triangle, the sum of the three medians is greater than the semi-perimeter of that triangle.
3) In any triangle, the sum of the three angle bisectors (terminated at the respective opposite side) is greater than the semi-perimeter of that triangle.
Which of 1, 2, and 3 are always true, and which are always false? Prove your answer.




Correct Solutions:

  1. Wei Fung. Alief Hastings HS, Houston, TX
  2. Justin Shih. Clear Lake HS, Houston TX
  3. Ken Tong. CNEC Christian College, Hong Kong, China
  4. Candice Hayes. Madisonville North Hopkins HS, Madisonville, KY
  5. Spencer Mortensen. Logan HS, Logan, UT
  6. Monica Hobson. Douglas HS, Winston, OR
  7. Joe Harn Chang. Wellington College, Wellington, New Zealand
  8. Carrie Darwin. Alcorn Central HS, Glen, MS
  9. Monica-Ramona Costache. Mihai Viteazul HS, Bucharest, Romania
  10. Alex Charsky. Douglas HS, Winston, OR
  11. Allen Rabinovich. Brooklyn Technical HS, Brooklyn, NY
  12. Joseph Cheng. Stuyvesant HS, New York, NY
  13. Natalie Goffi. St. Joseph Academy, Cleveland, OH
  14. Ariel Benson. Flatbush HS, Brooklyn, NY
  15. Alexandra Korolyova, Riga Secondary School No 40, Riga, Latvia


The Problem of the Week Contest Manual

Thirty-six of the best problems in blackline master form accompanied by the answers and solutions. For more information email Paragon Publications at jar@magicnet.net
The cost is $10.95 (which includes shipping)



Previous Problems

Check out the 3 other contests