InterviewSolution
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InterviewSolution
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Given that `Delta = 6, r_(1) = 3, r_(3) = 6` Inradius is equal toA. 2B. 1C. 1.5D. 2.5 |
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Answer» Correct Answer - B We have, `r_(1) = (Delta)/(s-a) = 2, r_(2) = (Delta)/(s-b) = 3, r_(3) = (Delta)/(s-c) = 6` Given `Delta =6`, `:. S-a = 3` ...(i) `s-b =2` ...(ii) `s-c =1` ...(iii) Adding Eqs. (i) and (ii), `2s - a - b =5 " or " a + b + c -a -b = 5 or c = 5` Adding Eqs. (i) and (iii), `2s - a- c = 4, or b = 4` And adding Eqs. (ii) and (iii), `2s -b -c = 3 or a = 3` Hence the sides of the `Delta` are `a =3, b = 4, c = 5` Since the triangle is right angled, the greatest angle is `90^(@)`. Also, the least angle is opposite to side a, which is `sin^(-1).(3)/(5)`. Therefore, `90^(@) - "sin"^(-1)(3)/(5) = "cos"^(-1)(3)/(5)` Also, `R = (abc)/(4Delta) = (60)/(24) = 2.5` `r = (Delta)/(s) = (6)/(6) = 1` |
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