If in the following figure, ∠ACB = 135° and the radius of the circle is 3\(\sqrt {2}\) cm, then the length of the chord AB is?

6

∠BDA = 180° - 135° = 45° (opposite angle in cyclic quadrilateral)

∠BDA = 45°

∠BOA = 2∠BDA = 2 × 45° = 90° (angle formed on center is double the angle formed on circumference by same are)

OB = OA = radius

AB = \(\sqrt {OB^2\;+\;OA^2}\) = \(\sqrt {18\;+\;18}\) = 6 cm