Trapezoid, circle

[Loki123]

So the trapezoid on the left is what we learned, that those sides will be equal. I am wondering whether that also goes for the triangle and whether the perimeter meets the side of the trapezoid or triangle at 90degrees like I marked it.

 

[Deleted member 4993]

So the trapezoid on the left is what we learned, that those sides will be equal. I am wondering whether that also goes for the triangle and whether the perimeter meets the side of the trapezoid or triangle at 90degrees like I marked it. View attachment 30713

..................trapezoid on the left is what we learned, that those sides will be equal.

Did you learn the proof of that corollary? If you did then you can easily disprove/confirm your conjecture about the triangle. Give it a try and let us know the result.

 

[Loki123]

..................trapezoid on the left is what we learned, that those sides will be equal.

Did you learn the proof of that corollary? If you did then you can easily disprove/confirm your conjecture about the triangle. Give it a try and let us know the result.

Not really, we were just told that lol

 

[Deleted member 4993]

Not really, we were just told that lol

Do a Google search with key-words "trapezoid around a circle" and learn the proof.

Please come back and tell us what you found - and how you would apply that to your present problem.

 

[Dr.Peterson]

So the trapezoid on the left is what we learned, that those sides will be equal. I am wondering whether that also goes for the triangle and whether the perimeter meets the side of the trapezoid or triangle at 90degrees like I marked it.

View attachment 30714

This is NOT true of trapezoids in general. Were you taught that this is true of isosceles trapezoids? Or do you not know the distinction?



Observe which pairs of segments are actually equal; it's not about the trapezoid, but about tangents. The same applies to the question of being perpendicular to the radius.

So, what is true for a triangle in general? What is true for an isosceles triangle in particular?

 

[Loki123]

This is NOT true of trapezoids in general. Were you taught that this is true of isosceles trapezoids? Or do you not know the distinction?

View attachment 30716

Observe which pairs of segments are actually equal; it's not about the trapezoid, but about tangents. The same applies to the question of being perpendicular to the radius.

So, what is true for a triangle in general? What is true for an isosceles triangle in particular?

Isosceles trapezoids... And from some digging I assume my theory is correct for only isosceles triangles...
However, with any trapezoid and triangle there are pairs of tangents that are equal between each other. For example in your pic, AX and AW... ZC and CY and so on

 

[Dr.Peterson]

Isosceles trapezoids... And from some digging I assume my theory is correct for only isosceles triangles...
However, with any trapezoid and triangle there are pairs of tangents that are equal between each other. For example in your pic, AX and AW... ZC and CY and so on

Correct. So the theorems you need to know, which immediately imply all these facts, are those given here:

Tangents and Circles - MathBitsNotebook(Geo)

The bigger theorem, which you haven't touched on, deals with the radius of a circle inscribed in a polygon:

Art of Problem Solving

artofproblemsolving.com