162. In AABC, if a2 + b2 + c = ac +...
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162. In AABC, if a2 + b2 + c = ac + ab 3, then (2) ñ r3 r_r3 L=12 rar (3) 14 + ra + rz = 2R + r (4) marz3 = 43

JEE/Engineering Exams
Maths
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Rearrange the equality as a quadratic in [ b^{2}-(a sqrt{3}) b+left(a^{2}-a c+c^{2}right)=0 ] The discriminant: [ begin{array}{l} Delta=(-a sqrt{3})^{2}-4left(a^{2}-cright. =-a^{2}+4 a c-4 c^{2} =-(a-2 c)^{2} leq 0 end{array} ] To admit a real solution for ( { }_{4} ) shas to be zero. That is Now, [ 3 c^{2}-2 b c sqrt{3}+b^{2}=0 Rightarrow b=c sqrt{3} ] Therefore, [ begin{array}{c} sqrt{a^{2}=b^{2}+c^{2}} end{array} ]
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