Mathematics
In the adjoining figure, ABCD is a square. Find the ratio between
(i) the circumferences
(ii) the areas of the incircle and the circumcircle of the square.
![In the figure, ABCD is a square. Find the ratio between (i) the circumferences (ii) the areas of the incircle and the circumcircle of the square. Mensuration, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.](https://cdn1.knowledgeboat.com/img/mla9/q26-c16-ex-16-3-mensuration-ml-aggarwal-solutions-icse-class-9-720x719.png)
Mensuration
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Answer
(i) Let side of the square be 2a units.
From figure,
![In the figure, ABCD is a square. Find the ratio between (i) the circumferences (ii) the areas of the incircle and the circumcircle of the square. Mensuration, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.](https://cdn1.knowledgeboat.com/img/mla9/q26-c16-ex-16-3-answer-mensuration-ml-aggarwal-solutions-icse-class-9-550x550.png)
AD = Diameter of incircle.
Radius of incircle (r) = = a units.
In right angle triangle ABC,
Using pythagoras theorem,
AC2 = AB2 + BC2
AC2 = (2a)2 + (2a)2
AC2 = 4a2 + 4a2
AC2 = 8a2
AC = units.
From figure,
AC is the diameter of circumcircle and AO is radius.
AO (R) = a units.
Hence, ratio between circumferences = .
(ii)
Hence, ratio between areas = 1 : 2.
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