Inscribed Angle Theorem Tangent Double Angle Tangent of Sum of Angle

Research Links

• Wikipedia: Inscribed angle
• Proof Wiki: Double Angle Formulas/Tangent
• PDF: DOUBLE-ANGLE, POWER-REDUCING, AND HALF-ANGLE FORMULAS
• Intersecting Chord Theorem for Ellipses – chords and other conical sections

 

By inspection from the above diagram:

 

Looking at this with the double angle tangent formula

  – the above is of this form.  Solving for x

 

 

 

 

 

Example 1: 

Using:      with   

 

     so    

Example 2: 

Using:        with      

 

Which brings me to questions about the multiplication of vectors