1.

Let `A B C D`be a quadrilateral with area `18`, side `A B`parallel to the side `C D ,a n dA B=2C D`. Let `A D`be perpendicular to `A Ba n dC D`. If a circle is drawn inside the quadrilateral `A B C D`touching all the sides, then its radius is`3`(b) 2(c) `3/2`(d) 1

Answer» With the given details, we can draw the diagram.
Please refer to video to see the diagram.
From the diagram,
In `Delta BEC`,
`BC^2 = BE^2+CE^2`
`=>(a-r+2a-r)^2 = (2r)^2 +a^2`
`=>a = 3/2r`
Now, area of the quadrilateral,
`(a*2r)+(1/2*a*2r) = 18`
`=>6ar = 36`
`=>ar = 6`
`=>3/2r^2 = 6`
`=>r^2 = 4`
`=>r = 2`
So, option `(b)` is the correct option.


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