Find the distance between the incentre and circumcentre of a triangle whose sides are 6cm, 8 cm and 10 cm?
Answers
1) Find the inradius of the incircle of side 6, 8 & 10 :
Find the semi-perimeter : s = 1/2 ( a + b + c ) = 1/2 ( 6 + 8 + 10 ) = 12
To find the area of the triangle using Heron's formula : K =
K = 24
Inradius r = K / s = 24 / 12 = 2 cm
2) To find circumradius:
R = abc / 4 = 480 / 96 = 5 cm
3) To find the difference between the circumcircle and incircle:
d² = R (R-2r) where R and r denote the circumradius and inradius respectively
d² = 5 (5-2(2))
d = √5 = 2.236 cm
Hope This Helps :)
Answer:
1) Find the inradius of the incircle of side 6, 8 & 10 :
Find the semi-perimeter : s = 1/2 ( a + b + c ) = 1/2 ( 6 + 8 + 10 ) = 12
To find the area of the triangle using Heron's formula : K =
K = 24
Inradius r = K / s = 24 / 12 = 2 cm
2) To find circumradius:
R = abc / 4 = 480 / 96 = 5 cm
3) To find the difference between the circumcircle and incircle:
d² = R (R-2r) where R and r denote the circumradius and inradius respectively
d² = 5 (5-2(2))
d = √5 = 2.236 cm