Question 865099
{{{drawing(465,300,-4.5,11,-0.5,9.5,
line(0,0,10,0),line(-3.62,9.32,6.38,9.32),
line(0,0,-3.62,9.32),line(10,0,6.38,9.32),
line(-3.62,9.32,10,0),
arc(10,0,20,20,180,248.755),
arc(-3.62,9.32,20,20,0,68.755),
locate(-4,9.5,A),locate(6.5,9.5,B),
locate(-0.4,0,D),locate(10.15,0,C),
locate(1.75,5.6,P),locate(4.63,3.62,Q),
green(line(0,0,6.38,9.32)),green(circle(3.18,4.66,0.1)),
locate(3.18,4.6,green(M))
)}}} You could just use Geometry and Trigonometry.
Because the figure involves a rhombus and arcs of circles with a rhombus side as a radius,
AQ = AB = AD = BC = DC = PC = 5 cm
and angle BAD = 1.2 radians.
AMB is a right triangle, with an angle at A that measures {{{1.2/2=0.6}}} radians.
AM = ABcos(0.6)
PM = MQ = AQ - AM = AB - ABcos(0.6) = AB(1-cos(0.6))
PQ = PM + MQ = 2MQ = 2AB(1-cos(0.6))
Since AB = 5 cm, the length of PQ, in cm, is
{{{2*5*cos(0.6)=1.7466}}}{{{(rounded)=highlight(1.75)}}} {{{"( rounded"}}}{{{to}}}{{{3}}}{{{significant}}}{{{"figures )"}}}