Question

In a triangle ABC, if a = 3, b = 4, c = 5, then the distance between its incentre and circumcentre is

• A. 1/2
• B.
• C. 3/2
• D.

Answer 1

The correct option is D

Given , a = 3, b = 4, c = 5

$\Rightarrow c^2=a^2+b^2\text{Therefore, it is right angled triangle at C}$

$\therefore R=\frac{1}{2}c=\frac{5}{2}andr=\frac{\Delta }{s}=\frac{\frac{1}{2}\times 3\times 4}{\frac{12}{2}}=1\therefore \text{Distance between incentre and circumcentre}=\sqrt{R^2-2Rr}=\sqrt{{\left(\frac{5}{2}\right)}^2-2.\frac{5}{2}}=\sqrt{\frac{5}{2}}\sqrt{\frac{5}{2}-2}=\frac{\sqrt{5}}{2}$