Given:
In the given diagram,
[tex]PD=3,DC=2,\text{ }and\text{ }BC=4[/tex]
To check:
AC a tangent line or not.
Explanation:
In a triangle PBC,
[tex]\begin{gathered} PB=3\text{ }(Since\text{ }PB=PD=radius) \\ BC=4 \\ PC=3+2=5 \end{gathered}[/tex]
Let us check the Pythagoras theorem,
[tex]\begin{gathered} PC^2=PB^2+BC^2 \\ 5^2=3^2+4^2 \\ 25=9+16 \\ 25=25 \end{gathered}[/tex]
It satisfies the theorem.
Therefore, the triangle PBC is a right-angle triangle.
That is, PB is perpendicular to AC.
So, AC is a tangent line.
Final answer:
Yes. AC is a tangent line.
