Question

. Three circles tangent externally to each other are tangent internally to a larger circle.
If one of the three circles has a radius of 5 cm and the circumscribing circle has a radius
of 10 cm, find the radii of the two other equal circles.

Answer 1

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Let x be the radius of Circle A  

Let y be the radius of Circle B  

Let z be the radius of Circle C

AB=x+y=10–eq.1

BC=y+z=14–eq.2

From eq.3,

z=16−x

Substituting this in eq.2

y+16–x=14

⟹y–x=1−eq.4

Solving eq.1 and eq.4

x=6

z=16−6=10

y=10−6=4

Radii of circles are 6,10 and 4A=z+x=16–eq.3

Answer 2

Let the radius of Circle A  = x

Let the radius of Circle B  = y

Let the radius of Circle C = z

It is given in question that ,

AB=x+y=10                                                        (eq-1)

BC=y+z=14                                                        (eq-2)

By the method of sustitution we get the value of z as

z=16−x                                                                (eq-3)

Substituting this in eq.2

                      y+16–x=14

                        ⟹y–x=1                                     (eq-4)

Solving  (eq-1) and   (eq-4) we get

x=6

substituting the value x=6 in eq 3

z=16−6

z =10

And

y=10−6

y =4

We get Radii of circles as x=6 , y=4 and z=10 of A, B and C circles