In the case of two intersecting circles of different radii, how many external common tangents are there?
2
Given: two circles of different radii that intersect each other at two points.
The number of common tangents between two circles depends on their relative position.
When two circles intersect at two distinct points, no tangent can pass between them, so there are no transverse (internal) common tangents.
However, two direct common tangents can still be drawn, one on each outer side of the circles.
These direct tangents are exactly the external common tangents.
Therefore the number of external common tangents is \(2\).
Hence, for two intersecting circles of different radii, the number of external common tangents is 2.
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