Question

$ABC$ is a circle with centre O. P is an external point in the line $AB$. From P, a tangent $PC$ has been drawn. If $AB=10cm,BP=8cm$, what is the measure of tangent $PC$?

• A. $24cm$
• B. $18cm$
• C. $12cm$
• D. $10cm$

Answer 1

The correct option is C $12cm$

$AB=10cmBP=8cmMP=13cm$

$M$ is the midpoint of $AB$ such that $AM=BM=5cm$

$OM=\sqrt{{\left(OA\right)}^2-{\left(AM\right)}^2}=\sqrt{r^2-25}{\left(OP\right)}^2={\left(OM\right)}^2+{\left(PM\right)}^2=r^2-25+{\left(13\right)}^2{\left(OP\right)}^2={\left(PC\right)}^2+{\left(CO\right)}^2=r^2+{\left(CO\right)}^2$

Equating both,

$CO=\sqrt{(13{)}^2-5^2}=\sqrt{144}=12cm$