Go Geometry: Problem 275: Right Triangle, Circumcircle, Sagitta, Inradius

Go Geometry: Problem 275: Right Triangle, Circumcircle, Sagitta, Inradius

Go Geometry: Elearn Geometry Problem 42

R.PradheepKanna
Draw a circle having its center B and radius AB.
Draw another Circle its Center C and Radius BC.
Let lower intersection of two circles is K
So, Triankgle BKC is a nequalteral.
so, ang.KBC=60deg, ang BCK=60deg
so, ang DCK=60-2α
since ang.DCK=2.ang DBK
ang.DBK=30-α
similerly, ang.BCD=2.angBKD
so ang.BKD=α
connect BD
according to symetrical property
ag.ABD=ang KBD
so, ang ABD also 30-α
Since ang ABC=X=ang.ABD+ang.KBD+ang.KBC
X=30-α+30-α+60
therefore X=120-2α