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Solution


Q.

Consider the following statements:

(i) If two circles touch internally then the distance between their centres is equal to the difference of their radii.

(ii) Distance moved by a rotating wheel in one revolution is equal to twice the circumference of wheel.

(iii) Area enclosed by two concentric circles of radius ‘r’ and ‘R’ (R > r), is π(R2-r2)

(iv) If two circles touch externally, then the distance between their centres is equal to the difference of their radii.

Which of the above statements are correct Choose the correct option from the following..
1 (i) and (ii)  
2 (ii) and (iii)  
3 (i) and (iii)  
4 (iii) and (iv)  

Ans.

(3)

Let two circles touch internally (see Fig.)

From the figure, AC=Rand BC=rAB=AC-BC=R-r ∴ Statement (i) is correct.Distance moved by a rotating wheel in one revolution=2πR=circumference of circle (see Fig. 12.5)∴ Statement (ii) is incorrect.From Fig. 12.6, area enclosed by two concentric circles of radius Rand r(R>r):=πR2-πr2=π(R2-r2)

∴ Statement (iii) is correct.Let two circles touch externally (see Fig. 12.7).From the figure,AC=AB+BC=r1+r2=distance between centresStatement (iv) is incorrect.