In quadrilateral ABCD,overline{AB} parallel o | vedclass

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(C) Since $\overline{AB} \parallel \overline{CD}$,$	riangle OAB \sim 	riangle OCD$ by $AA$ similarity criterion.Therefore,the ratios of their corres

Vedclass · Accepted Answer

$x = 8$ or $x = 11$

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(C) Since $\overline{AB} \parallel \overline{CD}$,$	riangle OAB \sim 	riangle OCD$ by $AA$ similarity criterion.Therefore,the ratios of their corresponding sides are equal: $\frac{OA}{OC} = \frac{OB}{OD}$.Substituting the given values: $\frac{3x - 19}{x - 3} = \frac{x - 4}{4}$.Cross-multiplying gives: $4(3x - 19) = (x - 3)(x - 4)$.$12x - 76 = x^2 - 7x + 12$.Rearranging into a quadratic equation: $x^2 - 19x + 88 = 0$.Factoring the quadratic: $(x - 8)(x - 11) = 0$.Thus,$x = 8$ or $x = 11$.

In quadrilateral $ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{O\}$. If $OA = 3x - 19$,$OB = x - 4$,$OC = x - 3$,and $OD = 4$,find the value of $x$.

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