Answers

2014-03-05T18:39:54+05:30
Let ABCD be a quadrilateral with center o.
join AO,BO,CO,DO.
The angle BAo,DAO is equal as AB and AD are tanglents 
let each angle equal = a;
The angles at B are similarly equal to each other. Let each of them equal b. 
Similarly for vertices C and D. 

The sum of the angles at the centre is 360 deg. 
The sum of the angles of ABCD is 360 deg. 

Therefore: 
2(a + b + c + d) = 360 
a + b + c + d = 180. 

From triangle AOB, angle BOA = 180 - (a + b). 
From triangle COD, angle COD = 180 - (c + d). 

Angle BOA + angle COD = 360 - (a + b + c + d) 
= 360 - 180 
= 180 deg. 

Thus AB and CD subtend supplementary angles at O.
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