A triangle has corners at $(3 , 4 )$ , $(6 ,7 )$ , and $(5 ,8 )$ . What is the radius of the triangle's inscribed circle?

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Answer 1 · 2018-04-28T18:05:44

$2sqrt2-sqrt5$ .

Let the vertices be $A(3,4), B(6,7) and C(5,8)$ .

Then, $AB^2=(3-6)^2+(4-7)^2=9+9=18$ , & likewise,

$BC^2=2 and CA^2=20$ .

$:. AB^2+BC^2=CA^2$ .

Hence, $DeltaABC$ is right-angled at $B$ .

From Geometry, we know that the inradius $r$ is,

$r=(AB+BC-CA)/2$ .

$=1/2(3sqrt2+sqrt2-2sqrt5)$ .

$:. r=2sqrt2-sqrt5$ .

A triangle has corners at (3 , 4 )(3 , 4 ), (6 ,7 )(6 ,7 ), and (5 ,8 )(5 ,8 ). What is the radius of the triangle's inscribed circle?