समकोण त्रिभुज ABC में `angleABC=90^(@)` AB = 5 cm तथा BC = 12 cm है। `DeltaABC` के बाह्य वृत्त की त्रिज्या ज्ञात करे?

Options

A. 7.5 cm
B. 6 cm
C. 6.5 cm
D. 7 cm

Answer

C

Explanation

According to question,

`ab=c^(2)/2`………….(i)
`therefore` In `DeltaABC`
Using pythagoras theorem
`AC^(2)=AB^(2)+BC^(2)`
`c^(2)=a^(2)+b^(2)` ……………….(i)
Put the value of `C^(2)` in equation, (i)
`2ab = a^(2)+b^(2)`
`a^(2)+b^(2)-2ab=0`
`(a-b)^(2)=0`
`therefore a-b=0`
a=b
If a=b means ABC is isosceles right anlged triangle it means
`angleA = 45^(@)`
`angleB=45^(@)`