True or false
Tangent circles always have exactly one common tangent.
False. Draw two tangent circles.
If one is not inside the other, then there is a tangent line that passes between the circles, touching each at the point of tangency.
There are also two lines that lie outside the circles, but lean up against both of them. Those are also common tangents.
If one circle is inside the other, then there is just a single common tangent.
If the area of a rectangle is 50cm and two circles are inside which are tangent to each other and the rectangle's side. What is the radius?
False.
Tangent circles may have zero, one, or two common tangents, depending on their relative positions. If the circles do not intersect, they will have two common tangents. If the circles intersect at exactly one point, they will have one common tangent. And if the circles are concentric (one circle is inside the other), they will have zero common tangents.
False. Tangent circles can have zero, one, or two common tangents.
To understand this, let's explore the concept of tangent circles and their common tangents.
Two circles are said to be tangent to each other if they touch each other at exactly one point. This point is called the point of tangency.
When two circles are tangent to each other externally, they have exactly one common external tangent. This means that there is only one straight line that touches both circles at their respective points of tangency, without intersecting the circles elsewhere.
On the other hand, when two circles are tangent to each other internally, they have exactly one common internal tangent. Again, there is only one straight line that touches both circles at their respective points of tangency from the inside, without intersecting the circles at any other point.
However, it is important to note that two circles can also be tangent to each other at more than one point. In this case, they can have two common tangents. For example, consider a larger circle with a smaller circle placed inside it. The smaller circle is tangent to the larger circle at two points, and therefore, they have two common tangents.
So, in summary, tangent circles can have zero, one, or two common tangents, depending on the specific configuration of the circles.