The intersecting secants theorem says
[tex]PQ\cdot PR=PS\cdot PT[/tex]
[tex]\implies8(8+x)=4(24+4)[/tex]
[tex]\implies64+8x=112[/tex]
[tex]\implies8x=48[/tex]
[tex]\implies x=6[/tex]
It's clear from the image that [tex]PT=28[/tex], so the first option is correct.
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Same as in the first problem; the intersecting theorems says
[tex]NM\cdot NL=NO\cdot NP[/tex]
[tex]\implies5(5+x)=3(3+17)[/tex]
[tex]\implies25+5x=60[/tex]
[tex]\implies5x=35[/tex]
[tex]\implies x=7[/tex]
so the third option is correct.
