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Solution


Q.

In Fig, ABC is a right triangle, right angled at B with BC = 3 cm and AB = 4 cm. A circle with centre O and radius x cm has been inscribed in ΔABC.
1 1 cm  
2 2 cm  
3 3 cm  
4 4 cm  

Ans.

(1)

In right ΔABC, we have

AC2=AB2+BC2AC2=(4)2+(3)2=16+9AC2=25AC=5 cmNow, AD = AB – BD = (4 – x) cmAF=AD=4-x cm(Tangents drawn from an external point A)Also,EC=BC{–BE=3-xcmCF=EC=3-x cm(Tangents drawn from an external point C)AC=AF+CF=4-x+3-x5=7-2x2x=7-5=2x=1 cm