A) \[\frac{1}{2}\]
B) \[\frac{\sqrt{3}}{2}\]
C) \[\frac{3}{2}\]
D) \[\frac{5}{2}\]
E) \[\frac{\sqrt{5}}{2}\]
Correct Answer: E
Solution :
Given, \[a=3,b=4,c=5\] \[\Rightarrow \] \[{{c}^{2}}={{a}^{2}}+{{b}^{2}}\] Therefore, it is a right angled triangle at C. \[\therefore \] \[R=\frac{1}{2}c=\frac{5}{2}\] and \[r=\frac{\Delta }{s}=\frac{\frac{1}{2}\times 3\times 4}{\frac{12}{2}}=1\] \[\therefore \]Distance between incentre and circumcentre \[=\sqrt{{{R}^{2}}-2Rr}\] \[=\sqrt{{{\left( \frac{5}{2} \right)}^{2}}-2.\frac{5}{2}.1}\] \[=\sqrt{\frac{5}{2}}\sqrt{\frac{5}{2}-2}=\frac{\sqrt{5}}{2}\]You need to login to perform this action.
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