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Question
In the given figure, ∠QPR = 50° and ∠PQR = 60°. Show that : PN < RN
Solution
In the given ΔPQR,
PS < PR .....(Of all the straight lines that can be drawn to a given straight line from a point outside it, the perpendicular is the shortest)
PN < PR ....(i) (∵ PN < PS)
Also,
RT < PR .....(Of all the straight lines that can be drawn to a given straight line from a point outside it, the perpendicular is the shortest)
RN < PR .....(ii) (∵ RN < RT)
Dividing (i) bt (ii),
`"PN"/"RN" < "PR"/"PR"`
`"PN"/"RN" < 1`
PN < RN.
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