meaning of SQ &It: PQ

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meaning of SQ &It: PQ

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Now QT = PQ holds, if and only if, T lies on P and this is possible if and only if, when Ф = 0, but S is interior point so this is not possible.

Thus QT < PQ.

Also QT = QS cos(Ф)

So, QS cos(Ф) < PQ

Now if Ф ∈ (0, 90) then cos(Ф) ∈ (1, 0) Thus,

⇒ QS < ( PQ / cos(Ф) )

And if you remember the fact that when we divide any number by positive number smaller than one, the result is always greater than the number

⇒ ( PQ / cos(Ф) ) > PQ

Thus QS < PQ

And when Ф ∈ (90, 180) then cos(Ф) is negative, so QS cos(Ф) is negative thus QS < PQ.

Similarly prove the second one.