What is direct common tangent and transverse common tangent?

Direct and transverse common tangent The direct common tangents meet on the line passing through centres and divide it externally in the ratio of the radii. The transverse common tangents meet on the line passing through centres and divide it internally in the ratio of the radii.

What is the definition of direct common tangent?

A common tangent is called a direct common tangent if both the circles lie on the same side of it. The figures given below shows common tangents in three different cases, that is when the circles are apart, as in (i); when they are touching each other as in (ii); and when they are intersecting each other as in (iii).

What are common tangents?

A common tangent is a line that is tangent to two circles. A common tangent can be further divided into: Internal common tangents, which pass through the line segment joining the centers of the two circles. External common tangents, which do not pass through such a segment.

What are two common tangents?

Two Common Tangents: If two circles intersect each other at two points, they will have two common tangents.

What is the formula of common tangent?

For finding direct common tangents of two circles, find the point P dividing the line joining the centre externally in the ratio of the radii. Equation of direct common tangents is SS1 = T2 where S is the equation of one circle.

What is the difference between common tangent and tangent circles?

A common internal tangent intersects the line segment connecting the centers of the two circles whereas a common external tangent does not.

What does it mean when two circles are tangent?

A circle can be tangent to another circle, which means that those two circles touches at exactly one point.

How many common tangents do circles have?

There can be four common tangents to two circles. The tangents can be either direct or transverse. When the two circles neither intersect nor touch each other, there are four common tangents.

What is transverse tangent?

A common tangent is called a transverse common tangent if the circles lie on opposite sides of it. YZ is the other transverse common tangent as the circle with centre O lies above it and the circle with centre P lies below it. A transverse common tangent is possible only when the circles are apart.