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  • A circle touches all the four sides of a quadrilateral ABCD. Prove that    

A circle touches all the four sides of a quadrilateral ABCD. Prove that  AB+CD=BC+DA

 

 

 

 
 
 
 
 

Answers (1)

To prove : AB+CD=BC+DA

Given :  OS=OP=OQ=OR= \text{radius of circle}

We know that the tangents drawn from exterior points of circle are equal. Hence 

AQ=AP\; \; \; -(i)

BQ=BR\; \; \; -(ii)

CS=RC\; \; \; -(iii)

DS=PD\; \; \; -(iv)

Adding (i), (ii), (iii) and (iv)

AQ+BQ+CS+DS=AP+PD+BR+RC

\Rightarrow AB+CD=AD+BC

Hence proved.

Posted by

Ravindra Pindel

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