MCQ
In the given figure, three circles with centres $A, B, C$ respectively touch each other externally. If $A B=5 cm , B C=7 cm$ and $C A=6 cm$, then 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.
$2 cm$
(b) : Let the radii of the three circles with centre $A$, $B$ and $C$ be $x, y, z$ respectively. Then,
$
x+y=5, y+z=7 \text { and } z+x=6
$Adding all three equations, we get
$
\begin{aligned}
& 2(x+y+z)=18 \Rightarrow x+y+z=9 \\
\therefore \quad & x=(x+y+z)-(y+z)=(9-7)=2 cm
\end{aligned}
$
$
x+y=5, y+z=7 \text { and } z+x=6
$Adding all three equations, we get
$
\begin{aligned}
& 2(x+y+z)=18 \Rightarrow x+y+z=9 \\
\therefore \quad & x=(x+y+z)-(y+z)=(9-7)=2 cm
\end{aligned}
$
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