Answer:
[tex]\text{A) }68\:\mathrm{cm}[/tex]
Step-by-step explanation:
The perimeter of a polygon is equal to the sum of all the sides of the polygon. Quadrilateral PTOS consists of sides TP, SP, TO, and SO.
Since TO and SO are both radii of the circle, they must be equal. Thus, since TO is given as 10 cm, SO will also be 10 cm.
To find TP and SP, we can use the Pythagorean Theorem. Since they are tangents, they intersect the circle at a [tex]90^{\circ}[/tex], creating right triangles [tex]\triangle TOP[/tex] and [tex]\triangle SOP[/tex].
The Pythagorean Theorem states that the following is true for any right triangle:
[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse, or the longest side, of the triangle
Thus, we have:
[tex]10^2+TP^2=26^2,\\TP^2=26^2-10^2,\\TP^2=\sqrt{576},\\TP=24[/tex]
Since both TP and SP are tangents of the circle and extend to the same point P, they will be equal.
What we know:
- [tex]TP=SP=24[/tex]
- [tex]TO=SO=10[/tex]
Thus, the perimeter of the quadrilateral PTOS is equal to [tex]24+24+10+10=\boxed{\text{A) }68\:\mathrm{cm}}[/tex]
