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Question
ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with the vertices as their centres. Find the radii of the three circles.
Solution
AB = 10 cm,
BC = 8 cm and
AC = 6 cm
Let the radii of three circle be r1, r2 and r3 ...(Shown in fig.)
r1 + r2 = 10 = AB ....(1)
r2 + r3 = 6 = AC ....(2)
r3 + r1 = 8 = BC .....(3)
Adding (1), (2) and (3), we get
2 (r1 + r2 + r3 ) = 10 + 6 + 8 = 24
r1 + r2 + r3 = 12 .....(4)
Subtract (4) and (1) ⇒ r3 = 12 - 10 = 2 cm
Subtract (4) and (2) ⇒ r1 = 12 - 6 = 6 cm
Subtract (4) and (3) ⇒ r2 = 12 - 8 = 4 cm
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