Geometry Books about 2D and 3D figures with explanations and problems?

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The discussion centers on seeking high school-level books that provide explanations and solutions for specific geometry problems. Key topics include the Exterior Angle Bisector Theorem, which states that the external angle bisector of a triangle divides the opposite side externally in the ratio of the sides containing the angle, typically applicable to non-equilateral triangles. Additionally, the discussion includes problems involving a cube and a regular tetrahedron, specifically calculating distances and lengths related to these shapes. Recommendations for suitable texts include Kiselev's geometry books and "The Art of Problem Solving: Introduction to Geometry" as well as "Euclidean Geometry in Mathematical Olympiads" by Evan Chen, with an emphasis on proof-heavy content being acceptable.
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I am looking for books that contain explanations (or to be able to answer) about something like this:

1) Exterior Angle Bisector Theorem
The external angle bisector of a triangle divides the opposite side externally in the ratio of the sides containing the angle. This condition occurs usually in non-equilateral triangles.

2) Given cube ABCDEFGH with side 2 units and line DF passes through plane ABGH at point T. Find distance ET

3) Given regular tetrahedron TABC with side 3 cm. M is mid point of AT and N is mid point of BC. Find length of MNAny books are ok but preferably high school level.

Thank you
 
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Is a proof-heavy text okay?
 
Muu9 said:
Is a proof-heavy text okay?
no problem
 
Try the two geometry books by Kiselev, or the Art of Problem Solving Introduction to Geometry or Euclidean Geometry in Mathematical Olympiads by Evan Chen
 
Thank you very much Muu9
 

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