A rectangle, a circle, and a triangle are drawn on a plane

Question

A rectangle, a circle and a triangle are drawn on a plane. What is the maximum possible number of points of intersection? The sides of the triangle are not collinear with any of the sides of the rectangle.

WhatsUp · Accepted Answer

Here is a proof that the answer by @Avi is the largest possible.
We have the following lemma, which is intuitively clear and also can be proved rigorously:

With the lemma, we now see that

and adding them together gives the maximum number.

Avi · Answer

Swiss Frank · Answer

Vassilis Parassidis · Answer

Draw a rectangle. Use the point of the intersection of the two diagonals as centre and and draw a circle with radius of length less than the distance from the intersection of the diagonals to one of the vertices, as shown. Then draw a triangle as shown. The number of points of intersection of the rectangle, the circle and the triangle is twenty.

A rectangle, a circle, and a triangle are drawn on a plane

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