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In adjoining figure o is the center of the circle.seg AB is diameter.at point CD is drawn from line BD is a tangent to the circle at point B then show that seg OD llchord AC​

Answer»

Step-by-step explanation:Given : O is the centre of the CIRCLE.Seg AB is a diameter, CD is the TANGENT at C.BD is a tangent at BIn ΔCOD and ΔBOD⇒OC=OB ....(Radii of same circle)⇒CD=DB ....(Tangent from an EXTERNAL point)⇒OD=OD ....(Common side)⇒ΔCOD=ΔBOD (SSS test)⇒ΔCOD=ΔBOD=x (c.a.s.t.) equation (i)In ΔAOC, AO=OC ....(Radii of same circle)⇒ ∠OAC=∠OCA=y ....(Isoceles Δ theorem) equation (II)⇒∠COB=∠OAC+∠OCA ....(Remote interior ∠ theorem)⇒∠COD+∠BOD=∠OAC+∠OCA⇒x+x=y+y ....[From equation (i) and (ii)]⇒2x=2y⇒x=y ....(dividing by 2)⇒∠COD=∠OCA⇒ Seg OD∥ chord AC. ....(Alternate ∠s test) Hence, PROVED.


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