What is the length of ST?

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Answer 1 · 2018-06-05T07:09:44

$ST=sqrt210 ~~14.49$ inches

By tangent-secant theorem , we have

$"(T angent)"^2="(Whole Secant)"$ $xx"(External Secant)"$

$i.e. TS^2=TQxxTR$

Tangent $=TS$

Whole Secant $=TQ==TR+RQ=7+23=30$ inches

External Secant $=TR=7$ inches

$rarrST^2=RTxxQT$

$toST=sqrt(RTxxQT$

$rarrST=sqrt(7xx30)=sqrt(210)~~14.49$ inches