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

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Showing 2 comments:
Math student
the answers are not proper. steps are missing.

Dr Math
you are right. 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.





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