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Laxman K.

asked • 04/03/15

What is the answer of this

Two congruent chords AB and CD which are not diameters, intersect at right angle in P. O is the centre of the circle. If M and N are the mid-points of AB and CD respectively, then prove that quadrilateral OMPN is a square.

1 Expert Answer

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Yohan C. answered • 04/03/15

Tutor
4 (1)

Math Tutor (up to Calculus) (not Statistics and Finite)

Yohan C.

The image (square) will look like first figure below with semi-circle:
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
From the first image, this is the main concept:
http://www.mathopenref.com/semiinscribed.html    (Thales Theorem)
 
Another concept will be similar triangles where you can find the lengths of smaller triangles from main triangle.
 
Good luck.
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04/03/15

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