Question

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if diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral prove that it is a rectangle..
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Answer 1

Step-by-step explanation:

Cyclic quadrilateral is a quadrilateral in which all its vertices touches the circle,

There is a property that Angle in a semicircle is 90°, which means that if the ends of a diameter makes an angle with the circle,it would be 90°.

Diagonal of the quadrilateral is also Serving as the diameter of the circle, and hence the other 2 vertices touching the circle at 90°.

Now as 2 out of 4 angles make 90° of the quadrilateral each, the other 2 angles will add up to 180° ( As angle sum property of a quadrilateral is 360° ). So the other 2 angles would also be 90° each.

Thus as all angles of this quadrilateral is 90°, It is a rectangle.

Answer 2

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