High School In a triangle, is the angle between the points of contact of the inscribed circle with the sides 120 degrees?

  • Thread starter Thread starter Antoha1
  • Start date Start date
Click For Summary
SUMMARY

The discussion centers on the geometric properties of a triangle, specifically whether the angle formed between the points of contact of the inscribed circle (incircle) with the triangle's sides can be 120 degrees. It is established that in a right triangle, the angle at the center of the incircle can be derived from the angles of the triangle itself. The inquiry also explores the relationship between the angles formed by the triangle's vertices and the angles at the center of the incircle.

PREREQUISITES
  • Understanding of triangle geometry
  • Familiarity with the concept of an inscribed circle (incircle)
  • Knowledge of angle relationships in triangles
  • Basic principles of Euclidean geometry
NEXT STEPS
  • Explore the properties of incircles in various types of triangles
  • Study the relationship between triangle angles and the angles at the center of the incircle
  • Investigate the implications of angle measures in right triangles
  • Learn about theorems related to inscribed angles and their properties
USEFUL FOR

Students of geometry, mathematics educators, and anyone interested in the properties of triangles and circles in Euclidean space.

Antoha1
Messages
19
Reaction score
2
in a triangle,is the angle between the points of contact of the inscribed circle with the sides 120 degrees? From drawings it might be similar to that but I am not sure
 
Mathematics news on Phys.org
Antoha1 said:
in a triangle,is the angle between the points of contact of the inscribed circle with the sides 120 degrees? From drawings it might be similar to that but I am not sure
Consider the case of a right triangle.
 
Von Mabit1 - Eigenes Werk, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=127735873
1920px-Produkt_Umfang_Inkreisradius.svg.webp


Imagine the blue angle would be 30°. Which angle is then at the blue center?
 

Similar threads

High School Inscribing a circle in an Oblique Square (Drafting)
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad What is the name of the triangle centre point with 120° subtended vertices?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Equation for circle points in 3D
  • · Replies 3 ·
Replies
3
Views
3K
MHB AO+BO+CO≥6r where r is the radius of the inscribed circle
  • · Replies 2 ·
Replies
2
Views
1K
MHB Difference of angles in a triangle
  • · Replies 4 ·
Replies
4
Views
2K
MHB Acute angle of right triangles
  • · Replies 4 ·
Replies
4
Views
2K
MHB Inscribed circle in the triangle
  • · Replies 2 ·
Replies
2
Views
2K
High School A triangle problem: Prove that |AC|+|AB|=|PR|+|PQ| given some constraints
  • · Replies 13 ·
Replies
13
Views
3K
MHB Find the distance between points C and D if the height of the tree is 4m
  • · Replies 1 ·
Replies
1
Views
2K
MHB Find the areas of segment in circle
  • · Replies 1 ·
Replies
1
Views
2K