A) \[\frac{AB}{BC}=\frac{PQ}{QR}\]
B) \[\frac{AB}{QR}=\frac{BC}{PQ}\]
C) \[\frac{AP}{BQ}=\frac{BQ}{CR}\]
D) \[\frac{AB}{PQ}=\frac{AP}{BQ}\]
Correct Answer: A
Solution :
Drop perpendicular ADE and PST from A and P to the other lines m and n. From two similar As ABD and ACE, \[\frac{AB}{AC}=\frac{AD}{AE}\] ?..(i) Also from similar \[\Delta \,s\] PSQ and PTB, \[\frac{PQ}{PR}=\frac{PS}{PT}\] ??(ii) Since \[AD=PS\] and \[AE=PT,\]therefore \[\frac{AB}{AC}=\frac{PQ}{PR}\] Applying dividendo, \[\frac{AB}{AC-AB}=\frac{PQ}{PR-PQ}\] or \[\frac{AB}{BC}=\frac{PQ}{OR}\]You need to login to perform this action.
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