Question

The inradius and circumradius of a triangle are 3.5 cm and 9 cm respectively. Find the distance between the incenter and circumcenter of the triangle. [Round up to two decimal places]

1. 4.23
2. 4.24
3. 4.26
4. 4.22

Answer 1

Correct Answer - Option 2 : 4.24

Given:

The inradius of circle = 3.5 cm 

The circumradius of circle = 9 cm 

Concept Used:

If the inradius of a triangle is (r_i) and the circum-radius is (r_c), then the distance between the incenter and circumcenter is √(r_c² – 2r_c × r_i)

Calculation:

Here inradius (r_i) = 3.5 cm

And circumradius (r_c) = 9 cm

Distance between incenter and circumcenter of the triangle is √(9² – 2 × 9 × 3.5)

⇒ √(81 – 63)

⇒ √18

⇒ 4.24 (up to two decimal places)

∴ The distance between the incenter and circumcenter of the triangle is 4.24 cm