Answer: x = 17
Explanation:
Given:
PR = 16
QR = RS
OQ = 9
PQ = x
Solve for x to nearest tenth
Solution:
OQ is the radius goes from center to end
PO is also the radius
Since OQ = 9 then
PO = 9
If PO = 9 then
OR = PR - PO
OR = 16 - 9
OR = 7
You can say ΔPRQ and ΔROQ are right triangle because QR and RS are the same. There is a rule that says when same and a radius hits it, then it creates a right angle
So you can solve for QR by pythagorean:
OQ² = OR² + QR²
9² = 7² + QR²
81 = 49 + QR²
QR² = 32
QR = √32
QR = 5.66
Now you can solve for x by pythagorean:
PQ² = PR² + QR²
x² = 16² + 5.66²
x² = 256 +32
x² = 288
x = 17