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we know that ∠ADO' = 90° ( since O'D is perpendicular to AC)
∠ACO= 90° ( OC(radius)perpendicular to AC(tangent))
In triangles ADO'and ACO ,
∠ADO' = ∠ACO ( each 90°)
∠DAO = ∠CAO (common)
by AA criterion ,triangles ADO' and ACO are similar to each other.
AO'/AO = DO'/CO ( corresponding sides of similar triangles )
AO = AO' + O'X + OX
= 3AO' (since AO'=O'X=OX because radii of the two circles are equal )
AO'/AO = AO'/3AO =1/3
DO'/CO=AO'/AO = 1/3
DO'/CO =1/3.
∠ACO= 90° ( OC(radius)perpendicular to AC(tangent))
In triangles ADO'and ACO ,
∠ADO' = ∠ACO ( each 90°)
∠DAO = ∠CAO (common)
by AA criterion ,triangles ADO' and ACO are similar to each other.
AO'/AO = DO'/CO ( corresponding sides of similar triangles )
AO = AO' + O'X + OX
= 3AO' (since AO'=O'X=OX because radii of the two circles are equal )
AO'/AO = AO'/3AO =1/3
DO'/CO=AO'/AO = 1/3
DO'/CO =1/3.
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