Answer:
See explanations below.
Explanation:
Theorem: In a circle, if a radius is perpendicular to a chord then the radius bisects the chord.
Using the theorem above and the given information, segment QS bisects segment PR.
PT = TR
PT = 12 cm (given)
TR = 12 cm (by the theorem above)
For QT, use the Pythagorean theorem.
The radius is given as 13 cm.
QP is a radius.
QP = 13 cm
(PT)² + (QT)² = (QP)²
12² + (QT)² = 13²
144 + (QT)² = 169
Subtract 144 from both sides.
(QT)² = 25
Take the square root of both sides.
√(QT)² = √25
QT = 5 cm
From the figure, we see that
QT + TS = QS
QS is a radius, so QS = 13 cm
5 + TS = 13
Subtract 5 from both sides.
TS = 8 cm
I hope the explanations are clear. If you have any questions, just ask in the comments.