turkey-yks 2013 Q36

turkey-yks · Other · ygs Circles Tangent Lines and Tangent Lengths
The method of drawing a tangent to a circle with center O from an external point P is given below.
  • Line segment OP is drawn.
  • The midpoint M of line segment OP is determined.
  • A circle with center M and diameter [OP] is drawn.
  • The intersection points of the circles with centers O and M are marked. Let one of these points be T.
  • Ray [PT is tangent to the circle with center O at point T.

In this construction, if the radii of the circles with centers O and M are 4 cm and 3 cm respectively, what is the length $| PT |$ in cm?
A) $3 \sqrt { 3 }$
B) $2 \sqrt { 5 }$
C) $\sqrt { 7 }$ 
The method of drawing a tangent to a circle with center O from an external point P is given below.

\begin{itemize}
  \item Line segment OP is drawn.
  \item The midpoint M of line segment OP is determined.
  \item A circle with center M and diameter [OP] is drawn.
  \item The intersection points of the circles with centers O and M are marked. Let one of these points be T.
  \item Ray [PT is tangent to the circle with center O at point T.
\end{itemize}

In this construction, if the radii of the circles with centers O and M are 4 cm and 3 cm respectively, what is the length $| PT |$ in cm?\\
A) $3 \sqrt { 3 }$\\
B) $2 \sqrt { 5 }$\\
C) $\sqrt { 7 }$
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