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Get Answers to all your Questions
Q: 7 If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.
Answers (1)
AC is the diameter of the circle.
Thus, $\angle A D C=90^{\circ}$ and $\angle A B C=90^{\circ}$--------1(Angle in a semi-circle is right angle)
Similarly, BD is the diameter of the circle.
Thus, $\angle B A D=90^{\circ}$ and $\angle B C D=90^{\circ}$--------2(Angle in a semi-circle is right angle)
From 1 and 2, we get
$\angle B C D=\angle A D C=\angle A B C=\angle B A D=90^{\circ}$
Hence, $A B C D$ is a rectangle.
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