Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 17"
(New page: ==Problem== {{empty}} ==Solution== {{solution}} ==See also== {{CYMO box|year=2006|l=Lyceum|num-b=16|num-a=18}}) |
(solution) |
||
Line 1: | Line 1: | ||
==Problem== | ==Problem== | ||
− | {{ | + | <div style="float:right"> |
+ | [[Image:2006 CyMO-17.PNG|250px]] | ||
+ | </div> | ||
+ | |||
+ | <math>ABC</math> is [[equilateral triangle]] of side <math>\alpha</math> and <math>AD=BE=\frac{\alpha}{3}</math>. The measure of the angle <math>\ang CPE</math> is | ||
+ | |||
+ | A. <math>60^{\circ}</math> | ||
+ | |||
+ | B. <math>50^{\circ}</math> | ||
+ | |||
+ | C. <math>40^{\circ}</math> | ||
+ | |||
+ | D. <math>45^{\circ}</math> | ||
+ | |||
+ | E. <math>70^{\circ}</math> | ||
==Solution== | ==Solution== | ||
− | {{ | + | Draw a segment <math>BF</math> such that <math>BF = \frac{\alpha}{3}</math>. By symmetry we see the triangle in the middle is equilateral, so the measure of <math>\ang CPE = 60^{\circ} \ \mathrm{(A)}</math>. |
==See also== | ==See also== | ||
{{CYMO box|year=2006|l=Lyceum|num-b=16|num-a=18}} | {{CYMO box|year=2006|l=Lyceum|num-b=16|num-a=18}} | ||
+ | |||
+ | [[Category:Introductory Geometry Problems]] |
Revision as of 16:43, 16 October 2007
Problem
is equilateral triangle of side and . The measure of the angle $\ang CPE$ (Error compiling LaTeX. ! Undefined control sequence.) is
A.
B.
C.
D.
E.
Solution
Draw a segment such that . By symmetry we see the triangle in the middle is equilateral, so the measure of $\ang CPE = 60^{\circ} \ \mathrm{(A)}$ (Error compiling LaTeX. ! Undefined control sequence.).
See also
2006 Cyprus MO, Lyceum (Problems) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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 |