Difference between revisions of "2007 Cyprus MO/Lyceum/Problem 15"
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==Problem== | ==Problem== | ||
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The reflex angles of the concave octagon <math>ABCDEFGH</math> measure <math>240^\circ</math> each. Diagonals <math>AE</math> and <math>GC</math> are perpendicular, bisect each other, and are both equal to <math>2</math>. | The reflex angles of the concave octagon <math>ABCDEFGH</math> measure <math>240^\circ</math> each. Diagonals <math>AE</math> and <math>GC</math> are perpendicular, bisect each other, and are both equal to <math>2</math>. | ||
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<math> \mathrm{(A) \ } \frac{6-2\sqrt{3}}{3}\qquad \mathrm{(B) \ } 8\qquad \mathrm{(C) \ } 1\qquad \mathrm{(D) \ } \frac{6+2\sqrt{3}}{3}\qquad \mathrm{(E) \ } \mathrm{None\;of\;these}</math> | <math> \mathrm{(A) \ } \frac{6-2\sqrt{3}}{3}\qquad \mathrm{(B) \ } 8\qquad \mathrm{(C) \ } 1\qquad \mathrm{(D) \ } \frac{6+2\sqrt{3}}{3}\qquad \mathrm{(E) \ } \mathrm{None\;of\;these}</math> | ||
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==Solution== | ==Solution== | ||
Revision as of 09:41, 8 May 2007
Problem
The reflex angles of the concave octagon 
measure 
each. Diagonals 
and 
are perpendicular, bisect each other, and are both equal to 
.
The area of the octagon is
Solution
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See also
| 2007 Cyprus MO, Lyceum (Problems) | ||
| Preceded by Problem 14 |
Followed by Problem 16 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
