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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