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The Centroid

Three circles...

Question

Three circles with centres $C_{1}, C_{2}, C_{3}$ and radii $r_{1}, r_{2}, r_{3}$ where $r_{1} < r_{2} < r_{3}$ are placed as shown in the figure.
Then $r_{2}$ =________

A

\sqrt{r_{3} - r_{1}}

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B

\sqrt{r_{3} + r_{1}}

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C

\sqrt{r_{1} r_{3}}

r3,r1

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D

\sqrt{r_{3}^{2} - r_{1}^{2}}

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Solution

The correct option is C $\sqrt{r_{1} r_{3}}$
The given circles with centers, $C_{1} < C_{2} < C_{3}$ are in GP,

with radius, $r_{1} < r_{2} < r_{3}$ respectively.

$∴ r_{2} = \sqrt{r_{1} r_{3}}$

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Similar questions

Q. Three Circles with centres

C_{1}, C_{2}, C_{3}

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

r_{1} < r_{2} < r_{3}

are placed as shown in the figure.
Then,

r_{2} =

Q. Three circles

C_{1}, C_{2}

C_{3}

r_{1}, r_{2}

r_{1} + r_{2}

respectively are such that

C_{1}

C_{2}

touch each other externally and

C_{3}

internally. Another circle with radius

r_{3}

touches all the three circles. If

r_{1} > r_{2} > r_{3}

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

are in A.P. then

{(\frac{r_{1}}{r_{2}})}^{3}

\frac{R_{1}}{r_{1}} + \frac{R_{2}}{r_{2}} + \frac{R_{3}}{r_{3}} =

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

are the radii of the escribed circles of a triangle

A B C

r

is the radius of its incircle,then

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

Q. Assertion :In a

Δ

r_{1} + r_{2} + r_{3} - r = 4 R

r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = Δ^{2}

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