Question

"Question 7 If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

Class 9 - Math - Circles Page 185"

Answer 1

Given: diagonals  NP &  QM of a cyclic quadrilateral NQPM are diameters of the circle passing through the vertices M, P, Q and N.

To Prove:

Quadrilateral NQPM is a rectangle.

Proof:

Here, ON= OP=OQ=OM ......(i)

[radii of same circle]

ON=OP= ½ NP....(ii)

OM=OQ= ½ MQ.....(iii)

From eq i ,ii, iii

NP=MQ

Hence, the diagonals of the quadrilateral NQPM equal and bisect each other. So quadrilateral NQPM is a rectangle.

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Hope this will help you......

Answer 2

Hi there!

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For solutions, Refer to the attached picture.
Regrets for handwriting _/\_

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Let's see some related topics :

⚫ Circle : The collection of all the points, which are at a fixed distance from a fixed point in a plane, is called a circle.

⚫ Radius : A line joining the centre to the Circumference of the circle, is called radius of a circle.

⚫ Secant : A line intersecting a circle at any two points, is called secant.

⚫ Diameter : A chord passing through the point of the circle, is called diameter. It is the longest chord.

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Thanks for the question !

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