Question : In $\triangle A B C, P$ and $Q$ are points on $AB$ and $BC$, respectively, such that $PQ\parallel AC$. Given that $AB=26, PQ=7$ and $AC=10$, then find the value of $AP$.
Option 1: 7.1
Option 2: 7.8
Option 3: 18.2
Option 4: 16.4
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Correct Answer: 7.8
Solution : In $\triangle A B C, PQ\parallel AC$. Also, $A B=26, P Q=7$ and $A C=10$ Since $PQ\parallel AC$, So, $\triangle ABC \sim \triangle PBQ$ ⇒ $\frac{AB}{BP}=\frac{AC}{PQ}$ ⇒ $\frac{26}{BP}=\frac{10}{7}$ ⇒ $BP = 26\times 0.7$ ⇒ $BP=18.2$ Now, $AB=BP+PA$ ⇒ $26=18.2+AP$ ⇒ $AP=26-18.2$ ⇒ $AP=7.8$ Hence, the correct answer is 7.8.
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