# Answer to Question #1347 in Analytic Geometry for jun- jun villanueva

Question #1347

Find the equation of the circle inscribed the triangle determind by the lines:2x-3y+21=0;3x-2y-6=0 and 2x+3y+9=0.

Expert's answer

Firstly, we have to find the points of intersection of thelines:

1. 2x-3y+21=0 and 3x-2y-6=0 :

(12, 15)

2. 2x-3y+21=0 and 2x+3y+9=0 :

(-7.5, 2)

3. 3x-2y-6=0 and 2x+3y+9=0 :

(0; -3).

As the equation of the circle is

R

we have the final system of equations for a and b:

(12-a)

144 + 225 – 24a -30b = 56.25 + 4 + 15a – 4b;

144+ 225 – 24a -30b = 9 – 6b.

308.75 = 39a + 26b;

360 = 24a +24b.

(-6.25, 21.25)

Thus R

1. 2x-3y+21=0 and 3x-2y-6=0 :

(12, 15)

2. 2x-3y+21=0 and 2x+3y+9=0 :

(-7.5, 2)

3. 3x-2y-6=0 and 2x+3y+9=0 :

(0; -3).

As the equation of the circle is

R

^{2}= (x-a)^{2}+ (y-b)^{2},we have the final system of equations for a and b:

(12-a)

^{2}+ (15-b)^{2}= (-7.5-a)^{2}+ (2 – b)^{2}(12-a)^{2}+ (15-b)^{2}=a^{2}+ (-3-b)^{2}144 + 225 – 24a -30b = 56.25 + 4 + 15a – 4b;

144+ 225 – 24a -30b = 9 – 6b.

308.75 = 39a + 26b;

360 = 24a +24b.

(-6.25, 21.25)

Thus R

^{2}= (12+ 6.25)^{2}+ (15-21.25)^{2}= 372.125**Answer: (x+6.25)**^{2}+ (y-21.25)^{2}=372.125Need a fast expert's response?

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Assignment Expert23.11.12, 09:41Dear visitor!

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