A private corporation launches a satellite into space. It plans to orbit the satellite at approximately 9200 miles above the surface of the Earth. Use the diagram of the satellite above the surface of the Earth and the fact that the radius of the Earth is approximately 3900 miles to determine the distance from the satellite to the point of tangency, T. Round your answer to the nearest whole number.

A. 5,990 miles
Incorrect. Recall the Secant-Tangent Product Theorem. Be sure that you find the length of the external segment of the secant and the total length of the secant.

B. 8,332 miles
Incorrect. Be sure that you have the correct lengths for the Secant segments. Remember, you are trying to find the length of the Tangent.

C. 10,978 miles
Correct! Great job taking the square root of the product of the external segment of the secant and the total length of the secant.

D. 13,100 miles
Incorrect. Remember that the relationship is with the length of the tangent and both the external and total length of the secant.

If AD has a length of 16 centimeters, then what is the perimeter of pentagon OYDAX?

A. 44 cm
Correct! If OX and OY are perpendicular bisectors and congruent, then AX and DY have the same lengths.

B. 36 cm
Incorrect. Use the information that you are provided with to determine the accurate length of DY. Use AX and OX to help you find that length.

C. 28 cm
Incorrect. Do not forget to include the length of AD in your total.

D. 20 cm
Incorrect. Be sure to find the length of DY and AD in your total. in your total.

Marco is given the following diagram of the cross-section of the hull of a submarine. From his diagram, he is given that AT = 12 feet, and TR = 3 feet. Use this information to find the width of the submarine at chord SQ. (Hint: You will need to use the Pythagorean Theorem.)

A. 18 feet
Correct! Using the Pythagorean Theorem, you found the length of ST or QT and then made sure to add both lengths for the total length of SQ.

B. 15 feet

Incorrect. Although the radius of this circle is 15 feet, it is not the length of SQ. Use the radius to create a triangle on SA.

C. 9 feet
Incorrect. Be sure you find the total length of both segments.

D. 3 feet
Incorrect. Since TR is given as 3 feet, and AR is the perpendicular bisector to SQ, the length of SQ must be larger than 3 feet. Use the radius to create a right triangle.

Determine the length of AB. If necessary, round your answer to the nearest tenth.

A. 3 units
Incorrect. Recall the relationship in the Intersecting Secant Theorem is a multiplicative relationship between the lengths of the segments in the secant.

B. 4 units
Correct! Great job remembering the Intersecting Secant Theorem!

C. 7.5 units
Incorrect. Remember that the relationship is between the length of the exterior segment of the secant and the total length of the secant. Make sure that you are using the correct measurements.

D. 12 units
Incorrect. Remember that the relationship is between the length of the exterior segment of the secant and the total length of the secant. Make sure that you are using the correct measurements.

Circle A represents a circular garden at a local university, and chords BC and DE represent two sidewalks through the garden that intersect at point F.

If BC = 15.6 meters, CF = 12 meters, and DF = 11.7 meters, what is the approximate length of the sidewalk represented by DE? Round your answer to the nearest tenth of a meter.

A. 3.6 meters
Incorrect. This number is the length of FB, which you will need to set up and solve an equation to calculate the length of EF.

B. 3.7 meters
Incorrect. This number is the length of EF, which is a portion of DE.

C. 15.4 meters
Correct!

D. 16.0 meters
Incorrect. BC = 15.6 meters, so to determine the length of FB, subtract CF from BC.