Find the length of PA - deductive Geometry

[chwala]

Homework Statement

see attached

Relevant Equations

Geometry

Text question is here and solution;

My approach;
$BP ×AP= PT^2$
Let $AP= x$
Therefore, $(6+x)x=16$
$x^2+6x-16=0$
$x=2$ or$x=-8$
$⇒x=2$ positive value only.

I guess this may be the only approach. Cheers!

 

[fresh_42]

Correct.

And the proof for the theorem you used: $BP \cdot AP = PT^2$ can be found on page 267ff. of the last attachment here:
https://www.physicsforums.com/threads/solution-manuals-for-the-math-challenges.977057/