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Question

# ABC is a triangle with AB=10 cm, BC=8 cm, and AC=6 cm. Three circles are drawn touching each other with the vertices of the triangle as their centres. The radius of the smallest circle is:

A
1 cm
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B
2 cm
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C
4 cm
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D
8 cm
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Solution

## The correct option is B 2 cmLet AP=AQ=x,QC=RC=y,BP=BR=z From the data given, we have: x+z=10 ... (i) y+z=8 ... (ii) x+y=6 ... (iii) (i) + (ii) + (iii) ⇒2(x+y+z)=24 ⇒x+y+z=12 ... (iv) From (i) and (iv), y=2 From (ii) and (iv), x=4 From (iii) and (iv), z=6 Hence, the radius of the smallest circle is 2 cm

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