In convex quadrilateral `A B C D ,A B=a ,B C=b ,C D=c ,D A=d` . This quadrilateral is such that a circle can be inscribed in it and a circle can also be circumscribed about it. Prove that `tan^2A/2=(b c)/(a d)dot`

Explanation

`a+c=b+d-(1)`

`/_A+/_C=180-(2)`

`In/_BAD`

`BD^2=a^2+d^2-2adcosA`

`In/_BCD`

`BD^2=b^2+c^2-2bccosC`

`a^2+d^2-2adcosA=b^2+c^2+2bccosA`

`a^2+d^2-b^2-c^2=2cosA(bc+ad)`

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