When is the angle of intersection of two circ | vedclass

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(C) The angle of intersection $	heta$ between two circles is given by $\cos 	heta = \frac{r_1^2 + r_2^2 - d^2}{2r_1r_2}$,where $r_1$ and $r_2$ are t

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They touch each other at only one point.

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(C) The angle of intersection $	heta$ between two circles is given by $\cos 	heta = \frac{r_1^2 + r_2^2 - d^2}{2r_1r_2}$,where $r_1$ and $r_2$ are the radii and $d$ is the distance between the centers.If $	heta = 0^{\circ}$,then $\cos 0^{\circ} = 1$.This implies $\frac{r_1^2 + r_2^2 - d^2}{2r_1r_2} = 1$,which simplifies to $r_1^2 + r_2^2 - d^2 = 2r_1r_2$.Rearranging gives $d^2 = r_1^2 + r_2^2 - 2r_1r_2 = (r_1 - r_2)^2$.Thus,$d = |r_1 - r_2|$.This condition represents the case where the two circles touch each other internally at a single point.

When is the angle of intersection of two circles $0^{\circ}$?

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