It is a well-known fact that the in- radius of a Pythagorean triangle (A right-triangle whose sides form a Pythagorean triple) is always an integer [1]. The purpose of this note is to extent this result in the following sense. If in any Pythagorean triangle a string of a finite number (say, k) of equal circles, inside the triangle, are so taken that i. each of the k circles touches a given side (other than the hypotenuse) ii. each of the (k-2) non-extreme circles also touch the two neighbouring circles. iii. the extreme two circles touch the nearest other side also.