ABC is a Right Triangle ,right angled at B. C(o,r) is the incircle and o is the incenter of the triangle.AB=5,BC=12,what is the radius of incircle?

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Answer 1 · 2018-05-17T11:31:45

Radius of the incircle is #2.0# unit

In Right Triangle the legs are #AB=P=5, BC=B=12#

Then hypotenuse is # H =sqrt(P^2+B^2)=sqrt(25+144)=13 #

In Right Triangle incircle radius is

#r = (P+B-H)/2=(5+12-13)/2=2.0#

Radius of the incircle is #2.0# unit [Ans]

Answer 2 · 2018-05-17T11:44:09

# 2#.

Observe that, the hypotenuse #AC=13#.

From Trigonometry, we know that, #Delta=rs#.

Here, #Delta="the Area of the triangle ABC"#,

#=1/2*AB*BC#,

#=1/2*5*12#,

#=30#,

#r="the inradius, and, "#

#s="semi-perimeter"#,

#=1/2(AB+BC+AC)#,

#=1/2(5+12+13)#,

#15#.

#:. r=Delta/s#,

#=30/15#,

#=2#,

as Respected Binayaka C. has readily derived!