If two circles have one point of intersection and the same radius, how many external tangents can be drawn?
2
Given: two circles with the same radius that meet at exactly one point of intersection.
Having a single common point with equal radii means the circles touch each other externally at that point.
When two circles touch externally, they have three common tangents in total.
One of these is the transverse tangent drawn at the point of contact, which is not an external tangent.
The remaining two are the direct or external common tangents, lying on the outer sides of the circles.
Since the radii are equal, these two external tangents are parallel to the line joining the centres.
Therefore the number of external tangents that can be drawn is \(2\).
Hence 2 external tangents can be drawn.
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