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Question

Three circles with centres A, B and C touch each other externally. If, AB = 5cm, BC = 7 cm and CA = 6 cm. Find the radii of the circles.

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Solution

Suppose radii of three circles be x, y , z cm

AB + BC + AC = 18 cm

x + y + y +z +z +x = 18 cm

x + y + z = 9 cm

Now, x + y = 5

And y + z = 7 cm

From (i) and (ii), we get z= 4 cm

From (iii) and (i), we get x = 2 cm

From (ii), we get y = 3 cm


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