Identify the value of x and the length of each secant segment. HELP PLEASE!!

Question

asked Aug 8, 2020 48.1k views

2 Answers

Juned Ansari · Answer 1 · 2020-08-14T04:03:54+0000

The intersecting secants theorem says

$PQ\cdot PR=PS\cdot PT$

$\implies8(8+x)=4(24+4)$

$\implies64+8x=112$

$\implies8x=48$

$\implies x=6$

It's clear from the image that
PT=28 , so the first option is correct.

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Same as in the first problem; the intersecting theorems says

$NM\cdot NL=NO\cdot NP$

$\implies5(5+x)=3(3+17)$

$\implies25+5x=60$

$\implies5x=35$

$\implies x=7$

so the third option is correct.