22.6 Contact of Circles

1.

Two circles touch externally if the distance between their centre is equal to the sum of their radii \(\,(d = c_1c_2)\,\), \(\, d = r_1 + r_2\)

2.

The circles touch (or are tangency) internally if \(\, d = r_1 - r_2\).

3.

The circles do not intersect if \(\, d> r_1 + r_2\,\) (each lies outside the other) or if \(\, d< \left |r_1 - r_2\right |\) (one lies wholly inside the other).

4.

The circles intersect at two distinct points if \(\,\left |r_1 - r_2\right | < d < r_1 + r_2\)

5.

Two circles are said to be orthogonal if they cut at right angles

The two circles are orthogonal if \(\,d^2 = r_1^2 + r_2^2\)
 

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