MCQ
In the given figure, three circles with centres $A, B, C,$ respectively, touch each other externally. If $AB = 5\ cm, BC = 7\ cm$ and $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 $2\ cm.$
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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