1. This presentation has been made for you by
FRANCISCO GUIJARRO BELDA
From Isaac Albéniz Secondary School
Leganés. Madrid. Spain.

2. COMMON EXTERNAL TANGENTS TO TWO GIVEN CIRCLES
1) Let s consider we already have the two circles, O1 and O2. The first step to
take is to join both centers, in red color in the image

3. 2) Draw the perpendicular bisector of O1O2 and you will get M, the middle
point of this segment

4. 3) Draw from M a circle (in green color in the image) with radius MO1

5. 4) Set aside segment r1 (in the upper side of the image below), radius of the circle O1.
Transfer upon this segment r2, radius of the circle O2. You will get r1-r2 (in red color),
which is going to become the radius of a new auxiliary circle. Keep in mind that this is
the subtraction of the two radius involved

6. 5) Draw a circle with center in O1 and radius r1-r2. You will get two intersection points
in the green color circle, Ta and Tb

7. 6) Join point O1 to Ta and extend the line until the black circle to get point T1 . Repeat
the process with O1 and Tb in order to get T2. Draw lines parallel to these ones from
O2 and you will get O2T3 and O2T4. Remember, O1T1 is parallel to O2T3 and O1T2 to
O2T4

8. 7) In order to finish, you only have to join point T1 to T3 and T2 to T4. You have the
solutions in blue color in the image below