If diagonal of a cyclic qdl are diameters of the circle are diametersof the circles through the vertices of the qdl then prove that it is a rectangle
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Hello mate =_=
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Solution:
It is given that ABCD is a cyclic quadrilateral. Also, AC and BD are two diameters of circle having centre O.
We need to prove that ABCD is a rectangle.
BD is a diameter which means that ∠BCD=∠DAB=90° ......... (1)
(Angle in a semi-circle is equal to 90°)
Similarly, AC is a diagonals which means that ∠ABC=∠ADC=90° .....(2)
(Angle in a semi-circle is equal to 90°)
From (1) and (2), we can notice that opposite angles of quadrilateral ABCD are equal which makes it a parallelogram.
Also, all the corner angles are equal to 90° which makes it a rectangle.
I hope, this will help you.
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