Relation between Inradius and Perimeter of Triangle
Three circles...
Question
Three circles touch each other externally. The distance between their centers is 5cm, 6cm and 7cm. Find the radii of the circles.
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Solution
Consider the given image wherein three circles touch each other externally.
Since the distances between the centres of these circles are 5cm,6cm and 7cm respectively, we have the following set of equations with respect to the above diagram x+y=5 .......(1) z+y=6 .......(2) 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 ⇒y=6−z=6−4=2
Therefore, the radii of the circles are 3cm,2cm and 4cm