question_answer

In AB = 5 cm, AC = 12 cm and \[AB\bot AC,\] then the radius of the circumcircle of \[\Delta ABC\] is          [SSC (CPO) 2014]

A) 6.5 cm

B) 6 cm 

C) 5 cm                

D) 7 cm

Correct Answer: A

Solution :

Given, \[\Delta ABC\] with \[AB=5\,\,cm,\] \[AC=12\,\,cm\]

and       \[AB\bot AC\]

Since, \[\angle BAC=90{}^\circ \]

So, BC is the diameter of the circle,[by property of semi-circle]

\[{{\text{(Hypotentuse)}}^{\text{2}}}\text{+(Perpendicular}{{\text{)}}^{\text{2}}}\text{+(Base}{{\text{)}}^{\text{2}}}\]

We have, \[B{{C}^{2}}=A{{B}^{2}}+A{{C}^{2}}\]

\[\Rightarrow \]\[B{{C}^{2}}={{5}^{2}}+{{12}^{2}}=25+144=169\]

\[\therefore \]      \[BC=13\,\,cm\]

\[\Rightarrow \]Radius \[=\frac{BC}{2}=6.5\,cm\]