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Using Lenz's Law

Check whether...

Question

Check whether the following statement is true/false

$\frac{1}{r_{1}} + \frac{1}{r_{2}} + \frac{1}{r_{3}} = \frac{s}{Δ} = \frac{1}{r}$ .

If true enter 1 else 0.

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Solution

we know that $r_{1} = \frac{Δ}{s - a}, r_{2} = \frac{Δ}{s - b}, r_{3} = \frac{Δ}{s - c}$ where $2 s = (a + b + c)$ and $Δ$ is the area of the triangle

$\frac{1}{r_{1}} + \frac{1}{r_{2}} + \frac{1}{r_{3}} = \frac{s - a + s - b + s - c}{Δ}$ $= \frac{3 s - (a + b + c)}{Δ} = \frac{s}{Δ} = \frac{1}{r}$
Hence given statement is True.

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