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 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.





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