If r1-r2 and r3 are thecorresponding exradii of a -ABC and r is the inradiiof the same triangle- then-1r1-1r2-1r3-1r

We nbsp;know nbsp;that,r1= nbsp;∆s a nbsp;, nbsp; nbsp;r2= nbsp;∆s br3= nbsp;∆s c nbsp;, nbsp; nbsp;r= nbsp;∆s1r1+1r2+1r3=1∆s a+1∆s b+1∆ ...

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In Radius

If r1,r2 and ...

Question

$If r_{1}, r_{2} and r_{3} are the corresponding exradii of a Δ ABC and r is the inradii of the same triangle, then - \frac{1}{r_{1}} + \frac{1}{r_{2}} + \frac{1}{r_{3}} = \frac{1}{r}$

True

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False

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Solution

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Similar questions

If r_{1}, r_{2} and r_{3} are the corresponding exradii of a Δ ABC and r is the inradii of the same triangle, then - \frac{1}{r_{1}} + \frac{1}{r_{2}} + \frac{1}{r_{3}} = \frac{1}{r}

If r_{1}, r_{2} and r_{3} are the corresponding exradii of a Δ ABC and r is the inradii of the same triangle, then - \frac{1}{r_{1}} + \frac{1}{r_{2}} + \frac{1}{r_{3}} = \frac{1}{r}

△ A B C, r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1}

r_{1}, r_{2}

r_{3}

2 s

A B C,

r_{1}, r_{2}, r_{3}

\frac{b c}{r_{1}} + \frac{c a}{r_{2}} + \frac{a b}{r_{3}} = k [\sum \frac{s}{a} - 3],

k

r_{1}, r_{2}, r_{3}

A B C

r

r_{1} r_{2} r_{3} - r (r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1})

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