A tangent is a line that passes through exactly one point on a circle. For any point on a circle, the radius and tangent line through that point are always perpendicular to each other making a right angle. If two triangles touch each other externally, then there will be 3 lines making right angle with radius of the circles at the point of intersection of circle and tangents. These three tangent lines are shown below. They are the black, blue and green ones.
We have been given an image two circles such as circle A externally tangent to circle B. We are asked to find the number of possible common tangents to circles A and B.
We know that tangent of a circle is a line that touches circle exactly at one place.
We can see both triangles touch each other externally. We know that maximum 3 common tangents can be drawn two two circles, when they touch each other externally.
Therefore, the answer of our given problem is 3 and option B is the correct choice.
