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29 May 2025, 04:22
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
87% (00:46) correct
12% (01:42) wrong based on 8 sessions
History
Date
Time
Result
Not Attempted Yet
If the length of chord \(PQ= 4\sqrt{2},\) what is the circumference of the circle with center O?
A. 4
B. 8
C. \(4π\)
D. \(8π\)
E. \(8π\sqrt{2}\)
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31 May 2025, 02:15
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OE
To find the circumference, we need the radius, which is either OP or OQ in this circle. We are given the length of PQ. PQ is a chord of the circle (it connects two points on the circle), but it’s also the hypotenuse of right triangle OPQ. Do we know anything else about that triangle? Since OP and OQ are both radii of the circle, they must have the same length, so the triangle is an isosceles right triangle. Using the ratio of the lengths of sides of a 45:45:90 right triangle, with PQ as the hypotenuse, the length of each radius is 4, making the circumference \(2πr\) or \(8π\), answer choice (D).
Answer: D
To find the circumference, we need the radius, which is either OP or OQ in this circle. We are given the length of PQ. PQ is a chord of the circle (it connects two points on the circle), but it’s also the hypotenuse of right triangle OPQ. Do we know anything else about that triangle? Since OP and OQ are both radii of the circle, they must have the same length, so the triangle is an isosceles right triangle. Using the ratio of the lengths of sides of a 45:45:90 right triangle, with PQ as the hypotenuse, the length of each radius is 4, making the circumference \(2πr\) or \(8π\), answer choice (D).
Answer: D
