Question

PS and PT are tangents to acircle, center O and radius10 cm, and meet at P. Thedistance PO = 26 cm.Calculate the perimeter ofthe quadrilateral PTOS.A.) 68 cmB.) 67.6 cmC.) 64 cmD.) 60 cm

Answer 1

Answer:

A. 68cm

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:

$PT=PS$

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