In the given figure, three circles with centres A, B, C, respecti… - Vidyadip

MCQ

In the given figure, three circles with centres $\text{A, B, C,}$ respectively, touch each other externally. If $\text{AB} = 5\ cm, \text{BC} = 7\ cm$ and $\text{CA} = 6\ cm,$ the radius of the circle with centre $A$ is:

A
$1.5\ cm$
✓
$2\ cm$
C
$2.5\ cm$
D
$3\ cm$

✓

Answer

Correct option: B.

$2\ cm$

Let the radii of the circle with centres $A, B$ and $C$ be $x, y,$ and $z$ respectively.
We know that radii of the same circle are equal.
$x + y = 5$
$y + z = 7$
$z + x = 6$
Adding the three equation, we get
$2(x + y + z) = 18$
$\Rightarrow x + y + z = 9$
$\Rightarrow x = 2$
So, the radius of the circle with centre $A$ is $2\ cm.$

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