<?xml version="1.0" encoding="utf-8"?>
<!-- More Geometry Snacks #12 (What Fraction is Shaded?), drawn by hand as a ruler-and-compass construction.
     A fixed figure: eight congruent triangles with four mirror lines leave the tip's height free, and the fraction
     changes with it, so the figure is the book's, whose triangles are equilateral (2026-11-06; it had a handle on the
     tip before). The square A B Q2 Q1 stands on the hidden points A and B (perpendiculars and circles of the side).
     The tip T above the top side is on the perpendicular bisector of AB, where the ray from Q1 at 75 degrees to the
     top side meets it: the bisector of the angle between Q1E, E the apex of the equilateral triangle on Q1Q2 (the
     circles about Q1 and Q2 through each other), and the side's perpendicular at Q1. The corner K1 of the octagon is
     on the diagonal through Q1, as far from Q1 as T is (a circle about Q1 through T), so the two shaded triangles at
     Q1 are congruent, and equilateral; the other tips and corners are its reflections in the diagonal, the vertical
     axis and the center O, which gives the octagon its four mirror lines. The eight triangles are the shaded ones,
     each a polygon of its own; the hole between them is the square with a white triangle on each side. -->
<Drawing Version="1">
  <Viewport Left="-5.2" Top="5.2" Right="5.2" Bottom="-5.2" />
  <Scene Left="-5.2" Top="5.2" Right="5.2" Bottom="-5.2" />
  <Styles>
    <ShapeStyle Name="Blue" Color="#FF0000FF" StrokeWidth="3" Fill="#FFB9B9FF">
      <Dark Color="#FF9DA3FF" Fill="#FF7F86D6" />
    </ShapeStyle>
  </Styles>
  <Figures>
    <FreePoint Name="A" Visible="false" Locked="true" X="-1" Y="-1" />
    <FreePoint Name="B" Visible="false" Locked="true" X="1" Y="-1" />
    <Segment Name="AB" Visible="false">
      <Dependency Name="A" />
      <Dependency Name="B" />
    </Segment>
    <PerpendicularLine Name="a" Visible="false">
      <Dependency Name="AB" />
      <Dependency Name="A" />
    </PerpendicularLine>
    <PerpendicularLine Name="b" Visible="false">
      <Dependency Name="AB" />
      <Dependency Name="B" />
    </PerpendicularLine>
    <Circle Name="ca" Visible="false">
      <Dependency Name="A" />
      <Dependency Name="B" />
    </Circle>
    <Circle Name="cb" Visible="false">
      <Dependency Name="B" />
      <Dependency Name="A" />
    </Circle>
    <IntersectionPoint Name="Q1" Visible="false" Algorithm="IntersectLineAndEllipse1">
      <Dependency Name="a" />
      <Dependency Name="ca" />
    </IntersectionPoint>
    <IntersectionPoint Name="Q2" Visible="false" Algorithm="IntersectLineAndEllipse1">
      <Dependency Name="b" />
      <Dependency Name="cb" />
    </IntersectionPoint>
    <MidPoint Name="O" Visible="false">
      <Dependency Name="Q1" />
      <Dependency Name="B" />
    </MidPoint>
    <MidPoint Name="M" Visible="false">
      <Dependency Name="Q1" />
      <Dependency Name="Q2" />
    </MidPoint>
    <SegmentBisector Name="axis" Visible="false">
      <Dependency Name="A" />
      <Dependency Name="B" />
    </SegmentBisector>
    <LineTwoPoints Name="diagonal" Visible="false">
      <Dependency Name="Q1" />
      <Dependency Name="B" />
    </LineTwoPoints>
    <!-- the tip T: the ray from Q1 at 75 degrees to the top side (halfway between the equilateral apex E at 60 and
         the perpendicular at 90) meets the axis -->
    <Circle Name="cq1" Visible="false">
      <Dependency Name="Q1" />
      <Dependency Name="Q2" />
    </Circle>
    <Circle Name="cq2" Visible="false">
      <Dependency Name="Q2" />
      <Dependency Name="Q1" />
    </Circle>
    <IntersectionPoint Name="E" Visible="false" Algorithm="IntersectCircleAndCircle2">
      <Dependency Name="cq1" />
      <Dependency Name="cq2" />
    </IntersectionPoint>
    <ReflectedPoint Name="Up" Visible="false">
      <Dependency Name="A" />
      <Dependency Name="Q1" />
    </ReflectedPoint>
    <AngleBisector Name="ray75" Visible="false">
      <Dependency Name="Q1" />
      <Dependency Name="E" />
      <Dependency Name="Up" />
    </AngleBisector>
    <IntersectionPoint Name="T" Visible="false" Algorithm="IntersectLineAndLine">
      <Dependency Name="ray75" />
      <Dependency Name="axis" />
    </IntersectionPoint>
    <Circle Name="ct" Visible="false">
      <Dependency Name="Q1" />
      <Dependency Name="T" />
    </Circle>
    <IntersectionPoint Name="K1" Visible="false" Algorithm="IntersectLineAndEllipse1">
      <Dependency Name="diagonal" />
      <Dependency Name="ct" />
    </IntersectionPoint>
    <ReflectedPoint Name="TL" Visible="false">
      <Dependency Name="T" />
      <Dependency Name="diagonal" />
    </ReflectedPoint>
    <ReflectedPoint Name="TB" Visible="false">
      <Dependency Name="T" />
      <Dependency Name="O" />
    </ReflectedPoint>
    <ReflectedPoint Name="TR" Visible="false">
      <Dependency Name="TL" />
      <Dependency Name="O" />
    </ReflectedPoint>
    <ReflectedPoint Name="K2" Visible="false">
      <Dependency Name="K1" />
      <Dependency Name="axis" />
    </ReflectedPoint>
    <ReflectedPoint Name="K3" Visible="false">
      <Dependency Name="K1" />
      <Dependency Name="O" />
    </ReflectedPoint>
    <ReflectedPoint Name="K4" Visible="false">
      <Dependency Name="K2" />
      <Dependency Name="O" />
    </ReflectedPoint>
    <Polygon Name="t1" Style="Blue">
      <Dependency Name="K1" />
      <Dependency Name="T" />
      <Dependency Name="Q1" />
    </Polygon>
    <Polygon Name="t2" Style="Blue">
      <Dependency Name="K1" />
      <Dependency Name="Q1" />
      <Dependency Name="TL" />
    </Polygon>
    <Polygon Name="t3" Style="Blue">
      <Dependency Name="K4" />
      <Dependency Name="TL" />
      <Dependency Name="A" />
    </Polygon>
    <Polygon Name="t4" Style="Blue">
      <Dependency Name="K4" />
      <Dependency Name="A" />
      <Dependency Name="TB" />
    </Polygon>
    <Polygon Name="t5" Style="Blue">
      <Dependency Name="K3" />
      <Dependency Name="TB" />
      <Dependency Name="B" />
    </Polygon>
    <Polygon Name="t6" Style="Blue">
      <Dependency Name="K3" />
      <Dependency Name="B" />
      <Dependency Name="TR" />
    </Polygon>
    <Polygon Name="t7" Style="Blue">
      <Dependency Name="K2" />
      <Dependency Name="TR" />
      <Dependency Name="Q2" />
    </Polygon>
    <Polygon Name="t8" Style="Blue">
      <Dependency Name="K2" />
      <Dependency Name="Q2" />
      <Dependency Name="T" />
    </Polygon>
  </Figures>
</Drawing>
