I want the proof for 10.10 theorem from circles
NCERT
Answers
A , B , C & D are concyclic
Step-by-step explanation:
10.10 theorem :
If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment , the four points lie on a circle i.e (they are concyclic)
A , B , C , D are 4 points ( no 3 of them are collinear)
Lets draw a circle passing through A , B , C with Center O.
Assume D does not lie on circle
and circle intersect AD at E
=> A , B , C & E are concyclic
now ∠ACB = ∠AEB ( Angle formed by same chord in same arc segment)
∠ACB = ∠ADB given
in Δ DEB
∠AEB = ∠EDB + ∠EBD
=> ∠AEB = ∠ADB + ∠EBD
=> ∠ACB = ∠ACB + ∠EBD
=> ∠EBD = 0°
=> E & D Coincide
A , B , C & E are concyclic
E & D coincide
=> A , B , C & D are concyclic
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Answer of this question (I want the proof for 10.10 theorem from circles
I want the proof for 10.10 theorem from circles NCERT)
