T or F two coplanar circles with two points of intersection will have four common tangents?
False - just two external tangents
False. Two coplanar circles with two points of intersection will have three common tangents.
To understand why, let's break it down step by step:
1. Two coplanar circles: We are given that we have two circles in the same plane.
2. Two points of intersection: Since the circles intersect at two points, we can visualize these circles as having a shape similar to the number "8" or an "infinity" symbol (∞). The two points where the circles cross each other are the points of intersection.
3. Common tangents: A tangent is a line that touches a circle at exactly one point, without intersecting it. Since the circles intersect at two points, it means that they share two common tangents—one on the interior of the circles and one on the exterior.
So, in conclusion, two coplanar circles with two points of intersection will have three common tangents, not four.