1.

AB and AC are the tangents of the circle with center O.Show that the quadrilateral ABOC is a cyclic quadrilateral.

Answer»

AB and AC are tangents

∠B = ∠C = 90°

∠B + ∠C = 180°

The sum of the four angles of a quadrilateral is 360°. 

ie, ∠A + ∠O = 180°

The opposite angles of quadrilateral ABOC are complementary.

∴ ABOC is a cyclic quadrilateral.



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