The three corners are A (1,2) B (5,2) and C (3,5)A(1,2)B(5,2)andC(3,5)
Distance between two points (x_1,y_1) and (x_2,y_2)(x1,y1)and(x2,y2)
is D= sqrt ((x_1-x_2)^2+(y_1-y_2)^2D=√(x1−x2)2+(y1−y2)2
Side AB= sqrt ((1-5)^2+(2-2)^2) =4 AB=√(1−5)2+(2−2)2=4unit
Side BC= sqrt ((5-3)^2+(2-5)^2) ~~3.61BC=√(5−3)2+(2−5)2≈3.61unit
Side CA= sqrt ((3-1)^2+(5-2)^2) ~~ 3.61CA=√(3−1)2+(5−2)2≈3.61unit
The semi perimeter of triangle is s=(AB+BC+CA)/2s=AB+BC+CA2 or
s= (4+3.61+3.61)/2~~ 5.61s=4+3.61+3.612≈5.61 unit
Area of Triangle is A_t = |1/2(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))|At=∣∣∣12(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))∣∣∣
A_t = |1/2(1(2−5)+5(5−2)+3(2−2))|At=∣∣∣12(1(2−5)+5(5−2)+3(2−2))∣∣∣ or
A_t = |1/2(-3+15+0)| = | 6.0| =6.0At=∣∣∣12(−3+15+0)∣∣∣=|6.0|=6.0 sq.unit
Incircle radius is r_i= A_t/s = 6.0/5.61 ~~1.07ri=Ats=6.05.61≈1.07 unit
Radius of the triangle's inscribed circle is 1.071.07 unit [Ans]
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