Quadrilateral `ABCD` is inscribed in a circle with `AD` as diameter. If `AD=4, AB=BC=1` then perimeter of quadrilateral `ABCD` is______

Answer

`00006.50`

Explanation

Let `/_ADC=alpha` and `AC=x`
By Cosine Rule
`x^(2)+1+1-(1)(1)cos(180^(@)-alpha)=2+ cosalpha=2+2 . (CD)/4`
`=2+ 1/2 sqrt(16-x^(2))impliesx=(sqrt(15))/2impliesCD=sqrt(16-x^(2))=7/2`
Perimeter `=4+2+7/2=19/2=9.50`