Question

Find the coordinate and radius of the center of the underlying circle of the triangle consisting of X axis, y axis and 3X + 4y = 24​

Answer 1

Answer:

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Step-by-step explanation:

Since the equation of line is given as  

3x+4y=24

⇒  

24

3x

​  

+  

24

4y

​  

=1

⇒  

8

x

​  

+  

6

y

​  

=1⟶(1)

since the line 3x+4y=24 meets on x-axis at A and on y-axis at B such that OA=8 and OB=6

∴AB=  

OA  

2

+OB  

2

 

​  

=  

64+36

​  

=10

areaofΔAOB=  

2

1

​  

.b.h=  

2

1

​  

.8.6=24squnit

Let the coordinate of centre of incircle be (r,r)

also,s=  

2

a+b+c

​  

=  

2

8+6+10

​  

=12

Now,r=  

s

arΔ

​  

=  

12

24

​  

=2

therefore coordinate of incircle is (2,2)