Given that the vertices A, B, C of a quadrilateral ABCD lie on a circle. Also A + C = 180°, then prove that the vertex D also lie on the same circle.
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Given. A+C=180° and A, B, C Lie on a circle
To prove. D lies on the same circle as A, B, C.
Soln. --
In a quadrilateral, if the sum of opposite angles is 180°, then it is a cyclic quadrilateral.
In quad. ABCD, A + C=180°,
Therefore, ABCD is a cyclic quad.
In a cyclic quad., the vertices lie on the same circle. Thus, D also lies on the same circle..
Hence, proved!
...............
Given. A+C=180° and A, B, C Lie on a circle
To prove. D lies on the same circle as A, B, C.
Soln. --
In a quadrilateral, if the sum of opposite angles is 180°, then it is a cyclic quadrilateral.
In quad. ABCD, A + C=180°,
Therefore, ABCD is a cyclic quad.
In a cyclic quad., the vertices lie on the same circle. Thus, D also lies on the same circle..
Hence, proved!
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