A triangle has corners at #(4 ,3 )#, #(1 ,9 )#, and #(6 ,3 )#. What is the radius of the triangle's inscribed circle?

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Answer 1 · 2017-11-21T11:50:45

The radius of the inscribed circle is #0.73# unit.

The three corners are #A (4,3) B (1,9) and C (6,3)#

Distance between two points #D= sqrt ((x_1-x_2)^2+(y_1-y_2)^2#

Side #AB= sqrt ((4-1)^2+(3-9)^2) ~~ 6.71#unit

Side #BC= sqrt ((1-6)^2+(9-3)^2) ~~7.81#unit

Side #CA= sqrt ((6-4)^2+(3-3)^2) = 2.0#unit

The semi perimeter of triangle is #s=(AB+BC+CA)/2# or

#s= (6.71+7.81+2.0)/2~~ 8.26# unit

Area of Triangle is #A_t = |1/2(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))|#

#A_t = |1/2(4(9−3)+1(3−3)+6(3−9))|# or

#A_t = |1/2(24+0-36)| = | -6.0| =6.0# sq.unit

Incircle radius is #r_i= A_t/s = 6.0/8.26 ~~0.73# unit [Ans]