Question
Three circles touch each other externally. The distance between their centres is 5 cm, 6 cm and 7 cm. Find the radii of the circles.
Answer: Option A
:
A
Consider the below figure wherein three circles touch each other externally.
Since the distances between thecentres of these circles are5 cm, 6 cm and 7 cm respectively, we have the following set of equations with respect to the above diagram:
x+y = 5 …..(1)
y+z = 6 ......(2) (⇒y=6-z)... (2.1)
x+z = 7 …..(3)
Adding (1), (2) and (3), we have 2(x+y+z)=5+6+7=18
⟹x+y+z=9....(4)
Using (1) in (4), we have 5+z=9⟹z=4
Now using, (3)⟹x=7−z=7−4=3
And (2.1)⟹y=6−z=6−4=2
Therefore, the radii of the circles are 3cm, 2cm and 4 cm.
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:
A
Consider the below figure wherein three circles touch each other externally.
Since the distances between thecentres of these circles are5 cm, 6 cm and 7 cm respectively, we have the following set of equations with respect to the above diagram:
x+y = 5 …..(1)
y+z = 6 ......(2) (⇒y=6-z)... (2.1)
x+z = 7 …..(3)
Adding (1), (2) and (3), we have 2(x+y+z)=5+6+7=18
⟹x+y+z=9....(4)
Using (1) in (4), we have 5+z=9⟹z=4
Now using, (3)⟹x=7−z=7−4=3
And (2.1)⟹y=6−z=6−4=2
Therefore, the radii of the circles are 3cm, 2cm and 4 cm.
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