1.

The length of side AB of quadrilateral ABCD having CD = 4, BC + AD = 10 units and inradius as a finite nonzero number will be:

Answer» Let the incircle touches the quadrilateral `ABCD` at points `P,Q,R and S`.
Please refer to video for the diagram.
We know tangents from a common point outside a circle is alays equal.
`:. DP = DS->(1)`
`CS = CR = CD-DS = 4-DS->(2)` (As CD = 4)
`BQ = BR->(3)`
`AQ = AP->(4)`
Also, we are given,
`BC+AD = 10`
From `(1),(2),(3),(4)`
`=>BR+CR+AP+DP = 10`
`=>BQ+4-DS+AQ+DS = 10`
`=>AQ+BQ = 6`
`=>AB = 6`


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