Question

A triangle has side lengths 18 cm, 24 cm and 30 cm. find the area of the triangle whose vertices are the incenter, circumcenter and centroid of that triangle.

Answer 1

`18^2 + 24^2 = 30^2`
`A(0,0) ,B(18,0) , C(0,24)`
centroid = `((0+0+18)/3, (24+0+0)/3)`
`= (6,8)`
circumcenter = MP of BC = `(18/2, 24/2) = (9,12)`
incenter (r) =` (area)/((1/2)perimeter)`
area = `1/2*24*18 = 216`
perimeter= `18+24+30 = 72`
so, incenter = `216/(72*1/2) = 6`cm
incenter=`(6,6)`
now for `(6,6), (9,12) ,(6,8) /_`
area= `1/2*b*h`
`= 1/2*2*3`
`= 3 cm^2 `
answer