Question

If two circles touch externally, how many common tangents can be drawn to them?
A. One
B. Two
C. Three
D. Four

Answer 1

Hint: We can draw three straight lines touching both the circles. Draw the circle and try to find all the 3 lines. Tangent is a straight line which touches the circle at a particular point. Try to find the lines, which touch both the circles and only at one point.

Complete step-by-step answer:

In the above figure, we can see that one tangent is passing from the point of contact of both the circles.

The second and third tangent is passing from the top and bottom point of both the circles.
Therefore, from two circles touching externally, three tangents can pass.
So, the correct answer is three.

Additional Information:
Tangent is a straight line which touches the circle at a particular point. The line from the centre of the circle and the tangent forms at 90 degree angle.
when considered two circles. There can be three tangents in common.
The one tangent will be at the point of touching where the two circles are touching each other. The point of contact of both the circles.
The second tangent will be at the bottom which will touch both the circles. The common tangent which is formed by touching the bottom ends of both the circles.
The third tangent will be at the top which will also pass by touching both the circles. The common tangent which is formed by touching the top ends of both the circles.
Therefore, The common tangents which can be drawn if two circles are touching externally at a single point = 3.

Note: Many a times, most of the students forget to take the two tangents which are touching the two circles from the top and the bottoms respectively. So, do consider that.