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

  • B
  • Thread starter Thread starter Antoha1
  • Start date Start date
AI Thread Summary
In a triangle, the angle formed between the points of contact of the inscribed circle with the sides is not universally 120 degrees; it varies based on the triangle's angles. The discussion explores this concept using a right triangle as an example. If one angle is 30 degrees, the angle at the center of the inscribed circle can be calculated accordingly. The relationship between the triangle's angles and the inscribed circle's contact points is crucial for understanding this geometric property. Overall, the angle between the points of contact is dependent on the specific triangle configuration.
Antoha1
Messages
15
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?
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Thread 'Six Pencil Puzzle'

Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
View full post »

Similar threads

B Inscribing a circle in an Oblique Square (Drafting)
Replies
9
Views
1K
I What is the name of the triangle centre point with 120° subtended vertices?
Replies
2
Views
929
I Equation for circle points in 3D
Replies
3
Views
3K
MHB Difference of angles in a triangle
Replies
4
Views
2K
B A Question Relating Sum of Angles and Breaking of the Parallel Postulate
Replies
6
Views
1K
B Is the following fact significant? (the factorisation of A^3 +/- B^3)
Replies
2
Views
1K
MHB Acute angle of right triangles
Replies
4
Views
1K
MHB Inscribed circle in the triangle
Replies
2
Views
2K
B Couple geometry/trigonometry questions
Replies
5
Views
2K
B Why do we need angle values greater than 90 degrees?
Replies
12
Views
4K

Hot Threads

Recent Insights

Back
Top