Question

Three circles touch each other externally. Find the radii of the circles if the sides of the triangle formed by joining the centres are 7 cm, 8 cm and 9 cm respectively.

Answer 1

$AB=x+y=7–eq.1$

$BC=y+z=8–eq.2$

$CA=z+x=9–eq.3$

From eq.3,

$z=9-x$

Substituting this in eq.2

$y+9–x=8$

$⟹x–y=1-eq.4$

Solving eq.1 and eq.4

$x=4$

$z=4-1=3$

$y=9-4=5$