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A cyclic quadrilateral is drawn such tha...

A cyclic quadrilateral is drawn such that three of its consecutive vertices are (0, 4), (0, 0) and (2, 0). Find the longest distance between any two vertices of this quadrilateral.

Text Solution

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On plotting the points on the graph paper, we see that 3 points A, O, B form a right angled triangle.
`therefore" "` AB is the diameter and we know that diameter is the longest chord of a circle . `" " (because` angle in a semicircle is right angle`)`
`therefore" "` Longest distance between any two vertices
`" "="Diameter"AB`
`" "=sqrt ((2-0)^(2)+(0-4)^(2))=sqrt(4+16)=2sqrt(5)` units
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