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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.
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
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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