How Can You Prove <)APB+<)CPD=180' in a Base-Quadrilateral Pyramid?

In summary, a tangent is a line or plane that touches a curved surface at only one point, a sphere is a three-dimensional shape that is perfectly round and has all points on its surface equidistant from its center, the tangent line to a sphere can be found by drawing a line from the point of tangency on the surface of the sphere perpendicular to the radius, a pyramid is a three-dimensional shape with a polygonal base and triangular faces that meet at a common point called the apex, and a sphere can be inscribed in a pyramid, with the vertices of the pyramid touching the surface of the sphere and the center of the sphere lying on the center of the base of the pyramid.
  • #1
menager31
53
0
There is a base-quadrilateraled pyramid ABCDS , which base is quadrilateral ABCD. Inscribed sphere is tangent in point P on the ABCD wall. Proof that

<)APB+<)CPD=180'


I don't like geometry and i really don't know how to start.
 
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  • #2
I guess you are participating both Physics and Mathematics Polish Olympiad... Try to ask this question on the website www.matematyka.org
 
  • #3
no I'm not
 
  • #4
That's interesting, because only about 2-3 of your threads are not connected to problems given to solve on the first levels of those olympiads...
 

1. What is a tangent?

A tangent is a line or plane that touches a curved surface at only one point, but does not intersect with the surface at that point.

2. What is a sphere?

A sphere is a three-dimensional shape that is perfectly round and has all points on its surface equidistant from its center.

3. How do you find the tangent line to a sphere?

The tangent line to a sphere can be found by drawing a line from the point of tangency on the surface of the sphere perpendicular to the radius of the sphere at that point.

4. What is a pyramid?

A pyramid is a three-dimensional shape with a polygonal base and triangular faces that meet at a common point called the apex.

5. What is the relationship between a sphere and a pyramid?

A sphere can be inscribed in a pyramid, meaning that the vertices of the pyramid touch the surface of the sphere, and the center of the sphere lies on the center of the base of the pyramid.

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