動態幾何

Pascal's Thm

If a hexagon is inscribed in a conic,the three pairs of opposite sides intersect one another in three collinear points.

How to find the tangent line of ellipse by Pascal's Thm?

Let A&B',C',C,A' and B be five points in the ellipse,respectively.

 

step 1:

Find the points Q and R as the following.

 

step 2:

The point P be the intersection point of the straight line through A,B' and the straight line through B,A'.

By Pascal's Thm,P is also on the straight line through Q,R.

So point P be the intersection point of the straight line through A,B' and the straight line through Q,R.

step 3:

Draw a straight line through A&B' and P.

Then the straight line through A&B' and P will be the tangent line of ellipse at point A&B'.

 

 

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