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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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