Question 1150085
<pre>
{{{drawing(400,400,-2.6,2.6,-2.6,2.6,
red(arc(-2,0,1.5,-1.5,0,33)),
circle(0,0,2), line(-2,0,2,0),locate(.81,2.03,K),

locate(-2.15,.1,A), locate(0,0,O), locate(2.05,.1,M),
locate(-1.6,.3,33^o),
line(-2,0,.8134732862,1.827090915),line(2,0,.8134732862,1.827090915))}}} 

∆AKM is a right triangle for it is inscribed in semicircle O.

AM = diameter of semi-circle O = 2R = 2(2) = 4

{{{"AK"/"AM"=cos(33^o)}}}
{{{AK = AM*cos(33^o)}}}
{{{AK = 4cos(33^o)}}}

{{{"KM"/"AM"=sin(33^o)}}}
{{{KM = AM*sin(33^o)}}}
{{{KM = 4sin(33^o)}}}

The perimeter of a triangle is the sum of the three sides.

{{{perimeter=AK+KM+AM}}}

{{{perimeter=4cos(33^o)+4sin(33^o)+4}}}

Approximately 9.533238412

Edwin</pre>