JEE Circles 1

Geometry Level 3

$C_1$ is a circle of radius 1 unit touching the x-axis and the y-axis. $C_2$ is another circle with radius $R>1$ and touching the axes and $C_1$ . Then calculate $\lfloor 1000R\rfloor$

This problem is a part of My picks for JEE 1

The answer is 5828.

1 solution

Niranjan Khanderia
Feb 3, 2015

O the center of the circle will be on x = y. From the origin the center of the small circle is $\sqrt2$ , and from this center that of big is (1 + R) away all on x=y. But the y coordinate of this O is =R.
$\sqrt2 + 1 + R = R*\sqrt2$ Solving for R we get 5.8284 hence the answer.

Thanks for the solution! Nice one!

Edit: Centre may also lie on $x+y=0$ . @Niranjan Khanderia

Pranjal Jain - 6 years, 4 months ago

Thanks. I have added your suggestion. There are four location for this configuration.

Niranjan Khanderia - 6 years, 4 months ago

Yes! 4 quadrants! $\ddot\smile$

Pranjal Jain - 6 years, 4 months ago

R will be 4.414

mridul jain - 6 years, 3 months ago

JEE Circles 1

This problem is a part of My picks for JEE 1

The answer is 5828.

1 solution

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