248,608 views
9 votes
9 votes
in the accompanying diagram, PA is tangent to the circle at A and PBC is a seacant. If PA= 2 square root 3 and PB =2, what is PC?

User Davebytes
by
2.7k points

1 Answer

14 votes
14 votes

PC = 6

Step-by-step explanation:

PA = 2 square root 3 = 2√3

PB = 2

PC = ?

We would apply secant-tangent theorem:


PA^2\text{ = }PB\text{ }*\text{ PC}
\begin{gathered} (2\surd3)^2\text{ = 2(PC)} \\ (2\surd3)(2\surd3)\text{ = 2PC} \\ 4(\sqrt[]{3})^2\text{ = 2PC} \\ 4(3)\text{ = 2PC} \end{gathered}
\begin{gathered} 12\text{ = 2PC} \\ \text{divide both sides by 2:} \\ (12)/(2)=(2PC)/(2) \\ PC\text{ = 6} \end{gathered}

in the accompanying diagram, PA is tangent to the circle at A and PBC is a seacant-example-1
User Howellmartinez
by
2.9k points