266 Strong’s Problenis. 
MATHEMATICS. 
<< 
Arr. XII. Mathematical Problems, with Geometrical Con- 
struetions and Demonstrations, by Professor THropork 
Srronc. 
OTRONG 
[Continued from page 64 of this Volume. } 
Prosiem [X. 
fr is required through a given point to describe a circle 
—, shall touch two circles given in position and magni- 
ey eee When the two circles are unequal, and the cir- 
cle which touches them does not circumscribe them 
Const. Let L (Fig. 1. pl. 2.) be the given point, and 
, HG, E the given circles. It is required to describe 
dan li a circle which shall touch the two given circles. 
Join the centres x, y, of the circles HBC, DGE by ay, 0 
extend wy till it meets FG, (FG being draw n, (Prob. v 
ase i.) touching the two circles) i in A. Let x dans os 
cut the apt circles in B, C, D, E. Through L the-given 
point, and C, D, thet two ‘adjacent ints, in which AE cuts 
i i ie circle LCD. Join 
Docistsvabions: For join AH, and xine it tll it meets 
the circle DG in It will meet this circle, because it cuts 
off similar sepments from the two given cireles, (Prob. ¥ vil.) 
And let AH meet the circle HLK in P. Now by the ae 
, Al, (Prob. viii. Cor. 4.) Therefore AH, AI==AL, 
ie But AL, AK=AH, Al’. Therefore AH, Al==AH, 
Al. Hence (striking out AH) AI==AI’. Wherefore ioe 
points I’, I coincide. Therefore the circle oer ets 
the ciréle DG, Ein I 
It also touches it in this point; for if se line MO be 
drawn touching KLH, BRH in H, and the line No. 2 touch- 
ing the circle LHI in [, then the angle RHM-=anegle in the 
