In ABC, if r = 1, R = 3 and S = 5, then the value of a^2 + b^2 + c^2 is

JEE MainMathematicsModerate

In $\Delta$ ABC, if r = 1, R = 3 and S = 5, then the value of
a^2 + b^2 + c^2 is

Show answer and solution

r = \frac{\Delta}{S} \Rightarrow \Delta = 5

\Delta = \frac{abc}{4R} \Rightarrow abc = 60

\Delta^{2}

= s(s - a) (s - b) (s - c)
5 = (5 - a) (5 - b) (5 - c)
= 125 - 25 (a + b + c) + 5(ab + bc + ca) - abc
a^2 + b^2 + c^2 =24

Source: Grass-G / M-24 Mathematics Paper 31 Dec.docx

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