How to make clipping geometry scale with the target?

Question

In the following example whenever Grid size is changed, the clipping region size remains as it is expressed in absolute coordinates.

<Grid Clip="M10,10 L10,150 L150,150 L150,10 Z">
    <Rectangle Fill="Red"/>
</Grid>

Is is possible somehow to clip the region such that the clipping geometry is scaled along with the clipped object?

Code behind solutions are not accepted, because this is to be used in the control template. Also, the region in the example is a simple shape for clarity sake. The actual used region is a complex and asymmetric shape.

EDIT:

It looks like I have to be more specific. This is the snipped that is part of custom control template for ProgressBar. When scaling the outer grid, the PART_Indicator rectangle does not scale its clipping region. The correct composition is when grid is sized 200x200.

<Grid>
    <Path Name="PART_Track" 
          Data="M100,0 A100,100 0 1 0 100,200 A100,100 0 1 0 100,0 Z"
          Fill="AliceBlue" Stretch="Fill"/>

    <Rectangle Clip="M100,0 A100,100 0 1 0 100,200 A100,100 0 1 0 100,0 Z"
               Stretch="Fill"
               Name="PART_Indicator" Fill="Red" 
               Height="100" VerticalAlignment="Top"/>

    <Path Name="Border" Data="M100,0 A100,100 0 1 0 100,200 A100,100 0 1 0 100,0 Z"
          Stretch="Fill" StrokeThickness="3" Stroke="Black"/>
</Grid>

UPDATE: Rick provided excellent suggestion, though it took time for me to understand how to use it. Here is the final code.

<Viewbox StretchDirection="Both" Stretch="Fill" >
    <Grid>
        <Path Name="PART_Track" 
              Data="M100,0 A100,100 0 1 0 100,200 A100,100 0 1 0 100,0 Z"
              Fill="AliceBlue" Stretch="Fill"/>

        <Border Clip="M100,0 A100,100 0 1 0 100,200 A100,100 0 1 0 100,0 Z"
                Height="200" VerticalAlignment="Bottom">
            <Rectangle Name="PART_Indicator" Fill="Red" VerticalAlignment="Bottom" 
                       Height="40"/>
        </Border>

        <Path Name="Border"
              Data="M100,0 A100,100 0 1 0 100,200 A100,100 0 1 0 100,0 Z"
              StrokeThickness="3"
              Stretch="Fill" Stroke="Black"/>
    </Grid>
</Viewbox>

Answer 1

Put the Grid inside of a Viewbox and change the size of the Viewbox instead of the Grid.

<Viewbox>
    <Grid Clip="M10,10 L10,150 L150,150 L150,10 Z" Width="200" Height="200">
        <Rectangle Fill="Red"/>
    </Grid>
</Viewbox>