Question

Find the distance between the incentre and circumcentre of a triangle whose sides are 6cm, 8cm and 10cm

Answer 1

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 =  $\sqrt{s(s−a)(s−b)(s−c)}$

K = 24

Inradius r = K / s = 24 / 12 = 2 cm

2) To find circumradius: 

R = abc / 4 $\sqrt{s(a+b-s)(a+c-s)(b+c-s)}$ = 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

Answer 2

Answer:

1) Find the in radius of the in circle 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

In radius r = K / s = 24 / 12 = 2 cm

2) To find circum radius:  

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