Question 996970
I am not going to write the units anywhere,
but we understand that all the numbers are measurements in inches.
I assume it is like this
{{{drawing(400,200,-10,30,-9.5,10.5,
circle(0,0,9.3),circle(27.38,0,2.4),
green(line(0,0,2.34,9)),
green(line(27.38,0,27.99,2.32)),
red(line(2.34,9,27.99,2.32)),
arrow(13.69,0,0,0),arrow(13.69,0,27.38,0),
locate(13.5,0,x),locate(13,5.66,red(26.5)),
locate(1.17,4.5,green(9.3)),locate(27.68,1.7,green(2.4)),
locate(27.7,1.72,green(2.4))
)}}} We have to find the missing {{{x}}} side measurement in that colorful quadrilateral in the middle.
The tangent to a circle is always perpendicular to the radius at the point if tangency,
so that quadrilateral has two right angles.
Let me draw that quadrilateral by itself,
tilted a bit, and enlarged a bit, so it shows its best profile.
You don't mind if I draw an extra red line parallel to the original red line, do you?
{{{drawing(500,200,-2.4,27.6,-10,2,
rectangle(0,0,0.4,-0.4),rectangle(26.1,0,26.5,-0.4),
red(line(0,0,26.5,0)),red(arrow(7,0,17,0)),
red(arrow(7,-2.4,17,-2.4)),red(arrow(7,-2.4,-7,-2.4)),
red(arrow(17,-2.4,30,-2.4)),
red(rectangle(0,-2.4,0.4,-2.8)),locate(13,-2.4,red(26.5)),
green(line(0,0,0,-9.3)),
green(line(26.5,0,26.5,-2.4)),
green(arrow(-0.9,-4,-0.9,0)),green(arrow(-0.9,-5,-0.9,-9.3)),
locate(13,0,red(26.5)),locate(0.1,-0.8,2.4),
locate(-1.8,-4,green(9.3)),locate(0.1,-5,9.3-2.4=6.9),
locate(26.6,-0.4,green(2.4)),
line(0,-9.3,26.5,-2.4),locate(13.2,-5.85,x)
)}}}
That extra red line made a right triangle appear.
The legs measure {{{red(26.5)}}} , and {{{green(9.3)-green(2.4)=6.9}}} .
The hypotenuse measures
{{{x=sqrt(26.5^2+6.9^2)=sqrt(702.25+47.61)=sqrt(149.68)=highlight(about27.4)}}}