InterviewSolution
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InterviewSolution
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In a right-angled isosceles triangle, the ratio of the circumradius andinradius is`2(sqrt(2)+1):1`(b) `(sqrt(2)+1):1``2:1`(d) `sqrt(2):1` |
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Answer» Sides of right angled isoceles triangle will be , `a,a and sqrt2a.` `:. Delta = 1/2*a*a = a^2/2` `s = (a+a+asqrt2)/2 = (a(2+sqrt2) )/2` `:.` Circumradius `(R) = (abc)/(4Delta) = (a*a*sqrt2a)/(4(a^2/2)) = a/sqrt2` Inradius `(r) = Delta/s = (a^2/2)/((a(2+sqrt2) )/2) = a/(2+sqrt2)` `:. R:r = a/sqrt2 : a/(2+sqrt2) = 2+sqrt2:sqrt2 = sqrt2+1:1` So, option `b` is the correct option. |
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