Inscribed circle

Write the equation of an incircle of the triangle KLM if K [2,1], L [6,4], M [6,1].

Correct answer:

x =  5
y =  2
r =  1

Step-by-step explanation:

k=(6−6)2+(4−1)2​=3 l=(2−6)2+(1−1)2​=4 m=(2−6)2+(1−4)2​=5 p=k+l+m=3+4+5=12 s=p/2=12/2=6 S=k⋅ l/2=3⋅ 4/2=6  x=(k⋅ 2+l⋅ 6+m⋅ 6)/p=(3⋅ 2+4⋅ 6+5⋅ 6)/12=5
y=(k⋅ 1+l⋅ 4+m⋅ 1)/p=(3⋅ 1+4⋅ 4+5⋅ 1)/12=2
r=S/s=6/6=1 (x−5)2+(y−2)2 = 1

Try calculation via our triangle calculator.


Try another example


Did you find an error or inaccuracy? Feel free to write us. Thank you!



Showing 1 comment:
Dr Math
The coordinates of the incenter are the weighted average of the coordinates of the vertices, where the weights are the lengths of the corresponding sides.





Tips for related online calculators
Looking for a statistical calculator?
See also our right triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:

Themes, topics:

Grade of the word problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: