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Question
In the figure, ABCD is a cyclic quadrilateral with BC = CD. TC is tangent to the circle at point C and DC is produced to point G. If angle BCG=108° and O is the centre of the circle, find: angle DOC
Solution
Join OC, OD and AC.
PCT is a tangent and CA is a chord.
∠ CAD = ∠ BCT = 54°
But arc DC subtends `∠`DOC at the centre and `∠`CAD at the remaining part of the circle.
∴ ∠ DOC = 2 ∠ CAD = 2 × 54° = 108°
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