Tangential Geometry

Tangential Geometry

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In this Task

  • A line will be drawn at an angle of 51° and to a length of 127.
  • Concentric circles will be added onto the end point of the new line.
  • Tangential lines will be used to connect the outer circles.

Associated Tasks

  • Single Line at angle.
  • Circle from center.
  • Lines which are tangential to circles.

Before you Start

  • Snaps are activated for this task. Use Window > Snaps to activate and deactivate snap modes.

Take Note

  • The LogiCursor automatically finds the tangent point on circles. Make sure the tangent snap is shown before starting or ending the line.

Single Line

Draw | Line | Single Line
The Single line tool can be used to draw a line at any length and angle. The length and angle information is input into the edit fields.

Start a line from the intersection shown below. Use the keyboard TAB key to access the edit fields and input a Length of 127 and an angle of 51, shown below.

Drawing a line at a specific length and angle

Circle from Center

Draw > Circle > Center Point Circle
This circle tool draws a single circle by defining the center point and diameter.
The diameter can either be defined by selecting a point in the graphics editor, or by inputting a value into the Diameter field.
The diameter of the circle can be changed after insertion by changing the value in the Diameter edit field.

Use the Circle from Center tool to insert two circles onto the endpoint of the newly drawn line. The diameters of these circles will be 21 and 50, shown below.

Inserting 2 circles on the endpoint of the new line

Tangent Lines using Single Line

Draw | Line | Single Line
Lines can be drawn tangentially to arcs and circles using the Single Line tool and the snap modes.
The snaps must be enabled with the Tan/Perp snap activated. Use Window > Snaps to check the current activation of snap modes.
The LogiCursor automatically finds the tangent point on circles. Make sure the tangent snap is shown before starting or ending the line.

Select the Line tool from the toolbar or use Draw > Line > Single Line.

Position the start of the line at the edge of the outer left circle, shown below. Do not allow the cursor to track to the intersection.

Finding the first tangent

 

Drag the cursor towards to tangential point on the middle circle. Left click only when both tangents are found, shown in the illustration below.

Tracking to corresponding tangencies

 

Repeat this action, this time finding the two tangential points on the circles shown below.

Connecting two tangents

Repeat this by connecting tangent lines on the lower side of the circles, shown below.

Four tangent lines connecting three circles

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