A direct common tangent of two circles is a straight line that touches both circles at exactly one point. This means that the tangent line is perpendicular to the radius of both circles at the point of tangency.
Finding the direct common tangent of two circles is important in various fields, such as geometry, engineering, and physics. It helps with determining the intersection points of two circles, which is useful in solving problems involving circles, such as calculating distances and angles.
The formula for finding the direct common tangent of two circles is (x-x1)(x-x2)+(y-y1)(y-y2)=r1^2-r2^2, where (x1,y1) and (x2,y2) are the coordinates of the centers of the circles, and r1 and r2 are the radii of the circles.
Yes, it is possible for two circles to have two direct common tangents if the circles are internally tangent (one circle is inside the other) or externally tangent (circles do not intersect but are close to each other).
A direct common tangent is a straight line that touches both circles at exactly one point, while a common tangent is a line that intersects both circles at two distinct points. Therefore, a direct common tangent is a special case of a common tangent.
