<?xml version="1.0" encoding="utf-8"?>
<!-- More Geometry Snacks #4 (Curiosity Closet), drawn by hand as a ruler-and-compass construction.
     The small semicircle stands on the hidden points L and T (its centre O1 is their midpoint); the two semicircles meet
     at T. The handle E, the far end of the large diameter, slides along a hidden stretch of the base line to the right
     of T, and O2 is the midpoint of TE. The common tangent of the two arcs: its midpoint M is where the perpendicular
     at T meets the circle on the diameter O1O2 (the tangent lengths from M are the geometric mean of the radii), and the
     tangent points T1 and T2 are T reflected in the lines MO1 and MO2. The blue square stands on T1T2, its far corners
     found with the line O1T1 (perpendicular to the tangent), the circle of radius T1T2 about T1 and a reflection in a
     midpoint. The dotted square stands under the small diameter LT (perpendiculars at L and T cut by the circle of
     radius LT and a parallel), the blue rectangle under the large diameter TE has the same height. The square and the
     rectangle have the same area for every E. -->
<Drawing Version="1">
  <Viewport Left="-1.2" Top="7.2" Right="8.8" Bottom="-2.8" />
  <Scene Left="-1.2" Top="7.2" Right="8.8" Bottom="-2.8" />
  <Styles>
    <PointStyle Name="Handle" Size="15" Fill="#FFFFFFFF" Color="#FF1E1E1E" StrokeWidth="2.5">
      <Dark Fill="#FF1E2228" Color="#FFF2F2F2" />
    </PointStyle>
    <ShapeStyle Name="Blue" Color="#FF0000FF" StrokeWidth="3" Fill="#FFB9B9FF">
      <Dark Color="#FF9DA3FF" Fill="#FF7F86D6" />
    </ShapeStyle>
    <ShapeStyle Name="DottedFrame" Color="#FF000000" StrokeWidth="3" Dash="Dot" IsFilled="false">
      <Dark Color="#FFE8EBF0" />
    </ShapeStyle>
    <LineStyle Name="Ink" Color="#FF000000" StrokeWidth="3">
      <Dark Color="#FFE8EBF0" />
    </LineStyle>
    <LineStyle Name="Dotted" Color="#FF000000" StrokeWidth="3" Dash="Dot">
      <Dark Color="#FFE8EBF0" />
    </LineStyle>
  </Styles>
  <Figures>
    <FreePoint Name="L" Visible="false" Locked="true" X="0" Y="0" />
    <FreePoint Name="T" Visible="false" Locked="true" X="2" Y="0" />
    <FreePoint Name="Z1" Visible="false" Locked="true" X="2.4" Y="0" />
    <FreePoint Name="Z2" Visible="false" Locked="true" X="8" Y="0" />
    <Segment Name="LT" Visible="false">
      <Dependency Name="L" />
      <Dependency Name="T" />
    </Segment>
    <Segment Name="Track" Visible="false">
      <Dependency Name="Z1" />
      <Dependency Name="Z2" />
    </Segment>
    <MidPoint Name="O1" Visible="false">
      <Dependency Name="L" />
      <Dependency Name="T" />
    </MidPoint>
    <PointOnFigure Name="E" Style="Handle" X="5.54" Y="0" Parameter="0.5607">
      <Dependency Name="Track" />
    </PointOnFigure>
    <MidPoint Name="O2" Visible="false">
      <Dependency Name="T" />
      <Dependency Name="E" />
    </MidPoint>
    <!-- the common tangent: its midpoint M on the perpendicular at T, at the geometric mean of the radii -->
    <MidPoint Name="Oc" Visible="false">
      <Dependency Name="O1" />
      <Dependency Name="O2" />
    </MidPoint>
    <Circle Name="cc" Visible="false">
      <Dependency Name="Oc" />
      <Dependency Name="O1" />
    </Circle>
    <PerpendicularLine Name="tT" Visible="false">
      <Dependency Name="LT" />
      <Dependency Name="T" />
    </PerpendicularLine>
    <IntersectionPoint Name="M" Visible="false" Algorithm="IntersectLineAndEllipse1">
      <Dependency Name="tT" />
      <Dependency Name="cc" />
    </IntersectionPoint>
    <LineTwoPoints Name="MO1" Visible="false">
      <Dependency Name="M" />
      <Dependency Name="O1" />
    </LineTwoPoints>
    <LineTwoPoints Name="MO2" Visible="false">
      <Dependency Name="M" />
      <Dependency Name="O2" />
    </LineTwoPoints>
    <ReflectedPoint Name="T1" Visible="false">
      <Dependency Name="T" />
      <Dependency Name="MO1" />
    </ReflectedPoint>
    <ReflectedPoint Name="T2" Visible="false">
      <Dependency Name="T" />
      <Dependency Name="MO2" />
    </ReflectedPoint>
    <!-- the square on the tangent -->
    <LineTwoPoints Name="O1T1" Visible="false">
      <Dependency Name="O1" />
      <Dependency Name="T1" />
    </LineTwoPoints>
    <Circle Name="c4" Visible="false">
      <Dependency Name="T1" />
      <Dependency Name="T2" />
    </Circle>
    <IntersectionPoint Name="S4" Visible="false" Algorithm="IntersectLineAndEllipse2">
      <Dependency Name="O1T1" />
      <Dependency Name="c4" />
    </IntersectionPoint>
    <MidPoint Name="M24" Visible="false">
      <Dependency Name="T2" />
      <Dependency Name="S4" />
    </MidPoint>
    <ReflectedPoint Name="S3" Visible="false">
      <Dependency Name="T1" />
      <Dependency Name="M24" />
    </ReflectedPoint>
    <Polygon Name="Square" Style="Blue">
      <Dependency Name="T1" />
      <Dependency Name="T2" />
      <Dependency Name="S3" />
      <Dependency Name="S4" />
    </Polygon>
    <!-- the dotted square and the rectangle under the diameters -->
    <PerpendicularLine Name="tL" Visible="false">
      <Dependency Name="LT" />
      <Dependency Name="L" />
    </PerpendicularLine>
    <Circle Name="cL" Visible="false">
      <Dependency Name="L" />
      <Dependency Name="T" />
    </Circle>
    <IntersectionPoint Name="Lb" Visible="false" Algorithm="IntersectLineAndEllipse2">
      <Dependency Name="tL" />
      <Dependency Name="cL" />
    </IntersectionPoint>
    <ParallelLine Name="par" Visible="false">
      <Dependency Name="LT" />
      <Dependency Name="Lb" />
    </ParallelLine>
    <IntersectionPoint Name="Tb" Visible="false" Algorithm="IntersectLineAndLine">
      <Dependency Name="tT" />
      <Dependency Name="par" />
    </IntersectionPoint>
    <PerpendicularLine Name="tE" Visible="false">
      <Dependency Name="LT" />
      <Dependency Name="E" />
    </PerpendicularLine>
    <IntersectionPoint Name="Eb" Visible="false" Algorithm="IntersectLineAndLine">
      <Dependency Name="tE" />
      <Dependency Name="par" />
    </IntersectionPoint>
    <Polygon Name="DottedSquare" Style="DottedFrame">
      <Dependency Name="L" />
      <Dependency Name="T" />
      <Dependency Name="Tb" />
      <Dependency Name="Lb" />
    </Polygon>
    <Polygon Name="Rectangle" Style="Blue">
      <Dependency Name="T" />
      <Dependency Name="E" />
      <Dependency Name="Eb" />
      <Dependency Name="Tb" />
    </Polygon>
    <Segment Name="SmallDiameter" Style="Ink">
      <Dependency Name="L" />
      <Dependency Name="T" />
    </Segment>
    <CircleArc Name="SmallArc" Style="Dotted">
      <Dependency Name="O1" />
      <Dependency Name="T" />
      <Dependency Name="L" />
    </CircleArc>
    <CircleArc Name="LargeArc" Style="Ink">
      <Dependency Name="O2" />
      <Dependency Name="E" />
      <Dependency Name="T" />
    </CircleArc>
  </Figures>
</Drawing>
