If the sides fo a triangle are in A-P- as well as in G-P- Then the value of r 1- r 2- r 2- r 3A- 1B- 0C- 2 rD- None

The correct option is B 0 2b= a+c, b^2 = ac ∴(a+c/2 )^2 = ac ⇒1/4 (a c)^2 =0 ∴ a=c 2b=2a ∴ a=b=c r_1= s/s a, r_2 = s/s b, r_3 = s/s c ∴ r_1=r_2=r_3 as a= ...

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Standard XII

Mathematics

Ex Radius

If the sides ...

Question

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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Solution

The correct option is B
0

$2 b = a + c, b^{2} = a c ∴ {(\frac{a + c}{2})}^{2} = a c \Rightarrow \frac{1}{4} (a - c)^{2} = 0 ∴ a = c 2 b = 2 a ∴ a = b = c r_{1} = \frac{s}{s - a}, r_{2} = \frac{s}{s - b}, r_{3} = \frac{s}{s - c} ∴ r_{1} = r_{2} = r_{3} as a = b = c ∴ \frac{r_{1}}{r_{2}} - \frac{r_{2}}{r_{3}} = 1 - 1 = 0$

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Similar questions

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

Q. If the sides of 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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Q. Let ABC be a triangle with incentre I and r. Let D, E, F be the feet of the perpendiculars from I to the sides BC, CA and AB respectively, If

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\frac{r_{1}}{r - r_{1}} + \frac{r_{2}}{r - r_{2}} + \frac{r_{3}}{r - r_{3}} = \frac{r_{1} r_{2} r_{3}}{(r - r_{1}) (r - r_{2}) (r - r_{3})}

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If the sides fo a triangle are in A.P. as well as in G.P. Then the value of r1r2−r2r3

The correct option is B 0 2b=a+c, b2=ac∴(a+c2)2=ac⇒14(a−c)2=0∴a=c2b=2a∴a=b=cr1=ss−a, r2=ss−b, r3=ss−c∴r1=r2=r3 as a=b=c∴r1r2−r2r3=1−1=0

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