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# please help with this circle theorem question?

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- Sky - VhinLv 62 months agoFavorite Answer
Observed that ABCD is a cyclic quadrilateral. In a cyclic quadrilateral, the sum of opposite angles is 180 degrees. A radius is perpendicular to a tangent. So angle DCO = 90 - 32 = 58 degrees

Since OB is parallel to the tangent line, triangle BCO is an isosceles right triangle with OB = OC = radius. So angle OCB = angle OBC = 45 degrees. Then angle DCB = angle DCO + angle OCB = 58 + 45 = 103 deg

So

angle DAB + angle DCB = 180

angle DAB + 103 = 180

angle DAB = 77 degrees

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