Circumscribed, Common tangent, Tangent circles

Question 1

What does it mean for a “polygon to be circumscribed about the circle” or “circle inscribed in the polygon”??

Answer 1

When each side of a polygon is tangent to a circle then the “polygon is to be circumscribed about the circle” and “the circle is inscribed in the polygon”

When each vertex of the polygon lies on the circle

Question 2

What is the difference between internal and external common tangents?

Answer 2

A common internal tangent intersects the segment joining the centers.

A common external tangent does not intersect the segment joining the centers.

Question 3

What are externally tangent circles?

What are internally tangent circles?

Answer 3

A circle can be tangent to a line, but it can also be tangent to another circle. Tangent circles are coplanar circles that are tangent to the same line at the same point.