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Given that a right angled trapezium has ...

Given that a right angled trapezium has an inscribed circle. Prove that the length of the right angled leg is the Harmonic mean of the lengths of bases

Text Solution

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Length of base=r+y,n+r
xy=`r^2`
`2/(1/(r+y)+1/(r+x))`
`(2(r+x)(r+y))/(2r+x+y)`
`(2(r^2+r(x+y)+xy))/(2r+x+y)`
`(4r^2+2r(x+y))/(2r+x+y)`
`(2r(2r+x+y))/(2r+x+y)`
`2r`.
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