First slide

Analysis of two circles in circles

Question

The radical axis of two circles having centres at C1 and C 2 and radii r1 and r2 is neither intersecting nor touching any of the circles, if

Moderate

A

$C_{1} C_{2} = 0$
B

$0 < C_{1} C_{2} < |r_{1} - r_{2}|$
C

$C_{1} C_{2} = |r_{1} - r_{2}|$
D

$|r_{1} - r_{2}| < C_{1} C_{2} < r_{1} + r_{2}$

Solution

The radical axis of two circles will neither intersect nor touch any of the given circles in the following cases:
(i) When $C_{1} C_{2} > r_{1} + r_{2}$ (ii) When $0 < C_{1} C_{2} < |r_{1} - r_{2}|$
Hence, option (b) is correct.

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