College

Line segment QP is tangent to the circle. What is the length of line segment QP? Round to the nearest unit.

A. 13 units
B. 17 units
C. 18 units
D. 20 units

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.