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Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point, as shown.

Asymptote code below

[asy]
unitsize(1.5 cm);


pair[] A;

for(int i = 1; i <= 10; ++i) {
A[i] = dir(90 - 360/10*i);
draw(dir(90 - 360/10*i)--dir(90 - 360/10*(i + 1)));
}

draw(A[10]--(A[10] + A[2] - A[3])--(A[10] + A[2] - A[3] + A[4] - A[5])--(A[10] + A[2] - A[3] + A[4] - A[5] + A[2] - A[1])--(A[10] + A[2] - A[3] + A[4] - A[5] + A[2] - A[1] + A[4] - A[3]));
draw((A[10] + A[2] - A[3])--(A[10] + A[2] - A[3] + A[10] - A[1])--(A[10] + A[2] - A[3] + A[10] - A[1] + A[8] - A[9])--(A[10] + A[2] - A[3] + A[10] - A[1] + A[8] - A[9] + A[6] - A[7]));

dot(A[10]);
[/asy]


An equilateral triangle, a regular octagon, and a regular -gon, all with the same side length, also completely surround a point. Find .

Atroshus  Aug 28, 2017

Best Answer 

 #1
avatar+20153 
+3

Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point, as shown.

 

 

An equilateral triangle, a regular octagon, and a regular -gon, all with the same side length, also completely surround a point. Find .

 

 

regular 24-gon

 

laugh

heureka  Aug 29, 2017
 #1
avatar+20153 
+3
Best Answer

Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point, as shown.

 

 

An equilateral triangle, a regular octagon, and a regular -gon, all with the same side length, also completely surround a point. Find .

 

 

regular 24-gon

 

laugh

heureka  Aug 29, 2017

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