Prove that the angle bisectos of a cyclic quadrilateral forms another quadrilateral which is also cyclic.

Asked by  | 21st Feb, 2013, 10:58: PM

Expert Answer:

 
ABCD is a cyclic quadrilateral 
?A + ?C = 180° and ?B + ?D = 180° 
(?A + ?C)/2 = 90° and (?B + ?D)/2 = 90°
x + z = 90° and y + w = 90° 
In ?AGD and ?BEC, 
x + y + ?AGD = 180° and z + w + ?BEC = 180° 
?AGD = 180° – (x+y) and ?BEC = 180° – (z+w) 
?AGD + ?BEC = 360° – (x+y+z+w) = 360° – (90+90) = 360° – 180° = 180° 
?AGD+?BEC = 180° 
?FGH+?HEF = 180° 
The sum of a pair of opposite angles of a quadrilateral EFGH is 180°. 
Hence EFGH is cyclic

Answered by  | 22nd Feb, 2013, 04:51: PM

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