Question

ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm. Three circles are drawn touching each other with the vertices as their centres. Find the sum of the radii of the three circles.

• A. 7 cm
• B. 3 cm
• C. 25 cm
• D. 12 cm

Answer 1

The correct option is D

12 cm

Given: ABC is a triangle with AB = 10 cm, BC= 8 cm, AC = 6cm. Three circle are drawn with centre A,B and C touch each other at P,Q and R respectively.
To find: The radii of there circles.
Let PA = AQ = $x$
QC = CR = $y$
RB = BP = $z$
$\therefore$ $x$+$z$ = 10 ...(i)
$z$+$y$ =8 ...(ii)
$y$+$x$= 6 ...(iii)
Adding, 2($x$+$y$+$z$)= 24
$\Rightarrow x+y+z=\frac{24}{2}$ = 12 ...(iv)
Subtracting (i) from (iv), we get
$y$ = 12 -10 = 2
Subtracting (ii) from (iv), we get
$x$ = 12-8 = 4
Subtracting (iii) from (iv), we get
$z$ = 12-6 = 6
$\therefore$ Radii are 2 cm, 4 cm and 6 cm.
Sum of the radii = 2 + 4 + 6 = 12 cm