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CBSE Class 9 Answered

the vertices of parallelogram lie on the circle.Prove that diagonals are equal.can you pls explain.
Asked by Amrut Kurtkoti | 04 Mar, 2015, 06:34: PM
answered-by-expert Expert Answer

Let PQRS be a parallelogram.

As the vertices lie on the circle it is a cyclic parallelogram.


In a cyclic quadrilateral opposite angle are supplementary. 

begin mathsize 12px style angle Q space plus space angle S space equals space 180 degree space minus negative negative space left parenthesis 1 right parenthesis But space in space straight a space parallelogram comma space opposite space angles space are space equal. therefore space angle straight Q space equals space angle straight S Using space in space left parenthesis 1 right parenthesis angle straight Q space plus space angle straight Q space equals space 180 degree angle straight Q space equals space 90 degree As space opposite space angles space are space equal space we space space angle straight S space equals space 90 degree Similarly comma space space angle straight P space equals space space angle straight R space equals space 90 degree straight A space parallelogram space with space right space angles space is space straight a space rectangle. But space in space straight a space rectangle space the space diagonals space are space equal. Hence space PR space equals space QS. end style

Answered by | 04 Mar, 2015, 06:49: PM

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