TWO CIRCLES AND MUTUAL TANGENT
Given two circles with centres K and N , radius of them are
those circles meet them(the circles) in A and B . Find AB , if
and . Mutual tangent of
AB
2
.
=
KN
5
SOLUTION
AB
=
KN
2
x
⇒ =
y
5
2
5 2
⇒ y2 =
x
4
5
Case 1 : We have an external common tangent .
( It’ s the same if the circles intersect or not)
Pythagorean theorem ® triangle KND : y 2 = 7 2 + x 2 ⇒
5 2
x = 7 2 + x 2 ⇒ x = 14 .
4
Case 2 : We have a common internal tangent .
Pythagorean theorem ® triangle KNC : y 2 = 17 2 + x 2 ⇒
5 2
x = 17 2 + x 2 ⇒ x = 34 .
4