Question
In $\triangle\text{ABC},\ \angle\text{A}$ is obtuse, $\text{PB}\perp\text{AC}$ and $\text{QC}\perp\text{AB}$ Prove that:
$AB × AQ = AC × AP$
$AB × AQ = AC × AP$
✓
Answer
Then, $\triangle\text{APB}\sim\triangle\text{AQC} [$By $AA$ similarity$]$
$\therefore\frac{\text{AP}}{\text{AQ}}=\frac{\text{AB}}{\text{AC}} [$Corresponding parts of similar $\triangle$ are proportional$]$
$⇒ AP × AC = AQ × AB .....(i)$
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