Answer :
Answer:
20 units
Step-by-step explanation:
The complete question is attached in the image.
QP is tangent and MP is a secant.
The secant-tangent theorem tells us that the external part of secant multiplied by whole secant would be equal to the tangent squared.
Thus, we can say:
MP * NP = QP^2
So, we can write from the image and figure out QP:
[tex]MP * NP = QP^2\\(24+11.5)(11.5)=QP^2\\(35.5)(11.5)=QP^2\\408.25=QP^2\\QP=20.2[/tex]
Out of the answer choices, rounded, it will be
QP = 20 units
Final answer:
The length of the tangent line segment QP is 20 units, calculated using the Pythagorean theorem.
Explanation:
The question is asking to determine the length of a tangent line segment (QP) to a circle. To find this length, we can use the Pythagorean theorem since the radius and the tangent form a right angle at the point of tangency. Given the information x = OQ = 10√3 and OP = 10 units (as the radius of the semicircle), we can calculate the length of the tangent segment QP using the following formula: QP = √(OP² + OQ²).
Plugging in the given values, we get:
QP = √{(10)² + (10√3)²}
QP = √{(100) + (300)}
QP = √{400}
QP = 20 units
Therefore, the length of the tangent line segment QP is 20 units after rounding to the nearest unit.
