InterviewSolution
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InterviewSolution
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If in a triangle `r_1=r_2+r_3+r ,`prove that the triangle is right angled. |
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Answer» We have `r_(1) = r_(2) + r_(3) + r` or `r_(1) - r = r_(2) + r_(3)` `rArr (Delta)/(s -a) -(Delta)/(s) = (Delta)/(s -b) + (Delta)/(s -c)` or `(Delta a)/(s(s -a)) = (Delta (2s -b -c))/((s-b) (s-c)) = (Delta a)/((s-b) (s-c))` or `s(s -a) = (s -b) (s -c)` or `s^(2) - sa = s^(2) - (b + c) s + bc` or `2s (b + c-a) = 2bc` or `(a + b + c) (b + c-a) = 2bc` or `(b + c)^(2) - a^(2) = 2bc` or `b^(2) + c^(2) = a^(2)` Hence, the triangle is right angled |
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