<?xml version="1.0" encoding="utf-8"?>
<!-- More Geometry Snacks #9 (Sangaku), drawn by hand as a ruler-and-compass construction.
     A fixed figure: the radius 3 and the length 8 are given, which leaves the small circle no freedom (2026-11-06; it
     had a handle on the small circle's top before, which stretched the rectangle away from 8). The bottom-left corner
     A, the bottom tangency Q of the big circle and the bottom-right corner RB are the hidden base points, at 0, 3 and
     8: the center O is a radius AQ up the perpendicular at Q, the circle has radius OQ, T is its top (Q reflected
     through O), the top side is the parallel to AQ through T, the left and right sides the perpendiculars at A and
     RB. The small radius r is 11 - sqrt 96 (r² - 22 r + 25 = 0 from the right triangle of the centers): sqrt 96 is
     the geometric mean of 8 and 12 (a semicircle on 20, cut by the perpendicular at 8), 11 is 8 + 3, and r is laid
     back from 11 along the bottom. The small circle's top F is r left of the top-right corner RT, its center P is r
     below F, and it touches the top, the right side and the big circle. The book's page draws the rectangle nearer 9
     long. -->
<Drawing Version="1">
  <Viewport Left="-0.7" Top="8.4" Right="12.7" Bottom="-2.4" />
  <Scene Left="-0.7" Top="8.4" Right="12.7" Bottom="-2.4" />
  <Styles>
    <ShapeStyle Name="BlueFrame" Color="#FF0000FF" StrokeWidth="3" IsFilled="false">
      <Dark Color="#FF9DA3FF" />
    </ShapeStyle>
    <ShapeStyle Name="Frame" Color="#FF000000" StrokeWidth="3" IsFilled="false">
      <Dark Color="#FFE8EBF0" />
    </ShapeStyle>
  </Styles>
  <Figures>
    <FreePoint Name="A" Visible="false" Locked="true" X="0" Y="0" />
    <FreePoint Name="Q" Visible="false" Locked="true" X="3" Y="0" />
    <FreePoint Name="RB" Visible="false" Locked="true" X="8" Y="0" />
    <Segment Name="AQ" Visible="false">
      <Dependency Name="A" />
      <Dependency Name="Q" />
    </Segment>
    <LineTwoPoints Name="bottom" Visible="false">
      <Dependency Name="A" />
      <Dependency Name="Q" />
    </LineTwoPoints>
    <PerpendicularLine Name="atQ" Visible="false">
      <Dependency Name="AQ" />
      <Dependency Name="Q" />
    </PerpendicularLine>
    <Circle Name="aboutQ" Visible="false">
      <Dependency Name="Q" />
      <Dependency Name="A" />
    </Circle>
    <IntersectionPoint Name="O" Visible="false" Algorithm="IntersectLineAndEllipse1">
      <Dependency Name="atQ" />
      <Dependency Name="aboutQ" />
    </IntersectionPoint>
    <Circle Name="big" Style="Frame">
      <Dependency Name="O" />
      <Dependency Name="Q" />
    </Circle>
    <ReflectedPoint Name="T" Visible="false">
      <Dependency Name="Q" />
      <Dependency Name="O" />
    </ReflectedPoint>
    <ParallelLine Name="top" Visible="false">
      <Dependency Name="AQ" />
      <Dependency Name="T" />
    </ParallelLine>
    <PerpendicularLine Name="left" Visible="false">
      <Dependency Name="AQ" />
      <Dependency Name="A" />
    </PerpendicularLine>
    <IntersectionPoint Name="LT" Visible="false" Algorithm="IntersectLineAndLine">
      <Dependency Name="left" />
      <Dependency Name="top" />
    </IntersectionPoint>
    <PerpendicularLine Name="rightSide" Visible="false">
      <Dependency Name="AQ" />
      <Dependency Name="RB" />
    </PerpendicularLine>
    <IntersectionPoint Name="RT" Visible="false" Algorithm="IntersectLineAndLine">
      <Dependency Name="rightSide" />
      <Dependency Name="top" />
    </IntersectionPoint>
    <!-- sqrt 96, the geometric mean of 8 and 12: the point at 12 is 4 (half of 8) past RB, the semicircle on the 20
         from A to the point at 20, about the point at 10 (midway between 8 and 12), is cut by the right side (the
         perpendicular at 8) at the height sqrt(8 * 12) -->
    <MidPoint Name="Four" Visible="false">
      <Dependency Name="A" />
      <Dependency Name="RB" />
    </MidPoint>
    <CircleByRadius Name="fourOn" Visible="false">
      <Dependency Name="A" />
      <Dependency Name="Four" />
      <Dependency Name="RB" />
    </CircleByRadius>
    <IntersectionPoint Name="Twelve" Visible="false" Algorithm="IntersectLineAndEllipse2">
      <Dependency Name="bottom" />
      <Dependency Name="fourOn" />
    </IntersectionPoint>
    <MidPoint Name="Ten" Visible="false">
      <Dependency Name="RB" />
      <Dependency Name="Twelve" />
    </MidPoint>
    <Circle Name="onTwenty" Visible="false">
      <Dependency Name="Ten" />
      <Dependency Name="A" />
    </Circle>
    <IntersectionPoint Name="Mean" Visible="false" Algorithm="IntersectLineAndEllipse1">
      <Dependency Name="rightSide" />
      <Dependency Name="onTwenty" />
    </IntersectionPoint>
    <!-- r = 11 - sqrt 96 along the bottom: the point at 11 is 3 (AQ) past RB, and sqrt 96 is laid back from it -->
    <CircleByRadius Name="threeOn" Visible="false">
      <Dependency Name="A" />
      <Dependency Name="Q" />
      <Dependency Name="RB" />
    </CircleByRadius>
    <IntersectionPoint Name="Eleven" Visible="false" Algorithm="IntersectLineAndEllipse2">
      <Dependency Name="bottom" />
      <Dependency Name="threeOn" />
    </IntersectionPoint>
    <CircleByRadius Name="meanBack" Visible="false">
      <Dependency Name="RB" />
      <Dependency Name="Mean" />
      <Dependency Name="Eleven" />
    </CircleByRadius>
    <IntersectionPoint Name="Radius" Visible="false" Algorithm="IntersectLineAndEllipse1">
      <Dependency Name="bottom" />
      <Dependency Name="meanBack" />
    </IntersectionPoint>
    <!-- the small circle: its top F is r left of the corner RT, its center P is r below F -->
    <CircleByRadius Name="rAboutRT" Visible="false">
      <Dependency Name="A" />
      <Dependency Name="Radius" />
      <Dependency Name="RT" />
    </CircleByRadius>
    <IntersectionPoint Name="F" Visible="false" Algorithm="IntersectLineAndEllipse1">
      <Dependency Name="top" />
      <Dependency Name="rAboutRT" />
    </IntersectionPoint>
    <PerpendicularLine Name="atF" Visible="false">
      <Dependency Name="top" />
      <Dependency Name="F" />
    </PerpendicularLine>
    <CircleByRadius Name="rAboutF" Visible="false">
      <Dependency Name="A" />
      <Dependency Name="Radius" />
      <Dependency Name="F" />
    </CircleByRadius>
    <IntersectionPoint Name="P" Visible="false" Algorithm="IntersectLineAndEllipse2">
      <Dependency Name="atF" />
      <Dependency Name="rAboutF" />
    </IntersectionPoint>
    <Circle Name="small" Style="BlueFrame">
      <Dependency Name="P" />
      <Dependency Name="F" />
    </Circle>
    <Polygon Name="rectangle" Style="Frame">
      <Dependency Name="A" />
      <Dependency Name="RB" />
      <Dependency Name="RT" />
      <Dependency Name="LT" />
    </Polygon>
  </Figures>
</Drawing>
