If the sides of a triangle ABC are in A-P as well as in G-P- then the value of r1r2-r2r3 is where r1-r2 and r3 are the radii of ex-circles-

∵ a,b,c are in A.P as well as in G.P. b^2=ac and a+c=2b ⇒(a+c)^2=4ac ⇒(a c)^2=0 ⇒ a=c ⇒ 2a=2b, a=b r_1=s a, r_2=s b, r_ ...

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Applications of Dot Product

If the sides ...

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If the sides of a triangle $A B C$ are in A.P as well as in G.P, then the value of $(\frac{r_{1}}{r_{2}} - \frac{r_{2}}{r_{3}})$ is (where $r_{1}, r_{2}$ and $r_{3}$ are the radii of ex-circles):

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If the sides fo a triangle are in A.P. as well as in G.P. Then the value of $\frac{r_{1}}{r_{2}} - \frac{r_{2}}{r_{3}}$

\frac{r_{1}}{r_{2}} - \frac{r_{2}}{r_{3}}

A B C,

r_{1}, r_{2}

r_{3}

r_{1} = 8, r_{2} = 12

r_{3} = 24,

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})

If the sides fo a triangle are in A.P. as well as in G.P. Then the value of $\frac{r_{1}}{r_{2}} - \frac{r_{2}}{r_{3}}$

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