Answer :

Given: a figure such that AB < OB and CD > OD


To prove: BAO > OCD


Consider ΔABO,


Given AB < OB


From figure, AB is opposite to AOB, and OB is opposite to OAB


But we know in a triangle the shortest side is always opposite the smallest interior angle and the longest side is always opposite the largest interior angle.


⇒∠AOB < OAB…………(i)


Now consider ΔCOD,


Given CD > OD


From figure, CD is opposite to COD, and OD is opposite to OCD


But we know in a triangle the shortest side is always opposite the smallest interior angle and the longest side is always opposite the largest interior angle.


⇒∠COD > OCD…………(ii)


From figure we can see that


AOB = COD……..(iii) (as they form vertically opposite angles)


Now substituting equation (iii) in equation (i), we get


⇒∠COD < OAB…………(iv)


Now comparing equation (ii) and equation (iv), we get


OAB > OCD


Or BAO > OCD


Hence Proved


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