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

Question

1835 views around the world

You can reuse this answer
Creative Commons License

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]

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