vela said:What are ex-radii? I've never heard that term before. Also, what are ##r## and ##R## supposed to denote?
utkarshakash said:Homework Statement
If in any triangle r=r1-r2-r3, then which type of triangle is it?
r1,r2,r3 denotes ex-radii.
The Attempt at a Solution
4R = r1+r2+r3-r
r2+r3 = 2R
I can't figure out what to do next.
Pranav-Arora said:Less encountered in geometry problems but they do exist. :)
http://en.wikipedia.org/wiki/Incircle_and_excircles_of_a_triangle
Hi utkarshakash! :)
You are almost there. Can you express ##r_2## and ##r_3## in terms of R, the sines and cosines of three angles of the triangle?
A triangle is a three-sided polygon that is formed by connecting three non-collinear points.
In a triangle, r1, r2, and r3 refer to the lengths of the three sides. They are usually labeled in alphabetical order, with r1 being the shortest side and r3 being the longest side.
The type of triangle can be determined by comparing the lengths of the three sides. If r1 = r2 = r3, then the triangle is an equilateral triangle. If only two sides are equal, then the triangle is an isosceles triangle. If all three sides are different, then the triangle is a scalene triangle.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This theorem is often used to determine if a triangle is a right triangle, as well as to find the lengths of the sides of a right triangle.
No, a triangle cannot have sides with negative lengths. The lengths of the sides must be positive numbers in order to form a valid triangle.