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Question
In the given figure, seg XY || seg BC, then which of the following statements is true?
Options
`"AB"/"AC" = "AX"/"AY"`
`"AX"/"XB" ="AY"/"AC"`
`"AX"/"YC" = "AY"/"XB"`
`"AB"/"YC" = "AC"/"XB"`
Solution
Given: seg XY || seg BC
`"AX"/"BX" = "AY"/"YC"` .......(By basic proportionality theorem)
⇒ `("BX"/"AX") + 1 = ("YC"/"AY") + 1`
⇒ `("BX" + "AX")/"AX" = ("YC" + "AY")/"AY"`
⇒ `"AB"/"AX" = "AC"/"AY"`
⇒ `"AB"/"AC" = "AX"/"AY"`
Hence, the correct option is `"AB"/"AC" = "AX"/"AY"`
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