please tell me quick tommorow my board exam is there
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Answer:
O
′
D is perpendicular to AC.
We know that ∠ADO
′
=90
Radius OC is perpendicular to tangent AC.
In ΔADO
′
and ΔACO,
∠ADO
′
=∠ACO (each 90 degree)
∠DAO=∠CAO (common)
By AA property, trangles ADO' and ACO are similar to each other.
AO
AO
′ =
CO
DO
′
(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
′
=
3AO
AO
′
=
3
1
CO
DO
′
=
AO
AO '
=
3
1
CO
DO =1/3
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