Answer:
A. 68cm
Step-by-step explanation:
PT and PS are tangents to circle O from point P.
Tangents to a circle from the same point are equal in length, therefore:
Next, the angle between the radius and tangent is 90 degrees.
Thus, triangle PTO is a right triangle with angle PTO=90 degrees.
Using Pythagoras theorem:
![\begin{gathered} PO^2=PT^2+TO^2 \\ 26^2=PT^2+10^2 \\ PT^2=676-100 \\ PT^2=576 \\ PT=24\operatorname{cm} \end{gathered}]()
Therefore, the perimeter of PTOS:
![\begin{gathered} \text{Perimeter}=PT+TO+OS+PS \\ =24+10+10+24 \\ =68\operatorname{cm} \end{gathered}]()
The correct choice is A.
Thus, triangle PTO is a right triangle with angle PTO=90 degrees