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Difficulty:
55%
(hard)
Question Stats:
51% (01:19) correct
49%
(01:18)
wrong
based on 63
sessions
History
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In the circle below, length of chord PQ is 40 units. What is the circumference of the circle?
(1) Angle PRQ = 90°.
(2) PR = 24 and QR = 32.
Attachment:
636613836662870759_9538604.PNG [ 4.55 KiB | Viewed 2083 times ]
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
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16 Apr 2019, 00:31
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Hi, I believe there's an error in the question; I am sure you meant the length of chord PQ (Not PR) is 40 units.
Statement 1: Angle PRQ = 90°
If angle PRQ is 90°, then the PQ must be the diameter since the angle in a semicircle is 90° (circle theorem)
So, diameter = 40 units, i.e. radius = 20 units. Therefore, the circumference of the circle is 2π x radius = 40π
Statement 1 is sufficient.
Statement 2: PR = 24 and QR = 32
Angles 24, 32, and 40 form a Pythagorean triplet. So, triangle PQR is a right-angled triangle, right-angled at angle R. Again, if angle PRQ is 90°, then the PQ must be the diameter since the angle in a semicircle is 90° (circle theorem)
So, diameter = 40 units, i.e. radius = 20 units. Therefore, the circumference of the circle is 2π x radius = 40π
Statement 2 is sufficient.
Therefore, the correct answer is D.
Statement 1: Angle PRQ = 90°
If angle PRQ is 90°, then the PQ must be the diameter since the angle in a semicircle is 90° (circle theorem)
So, diameter = 40 units, i.e. radius = 20 units. Therefore, the circumference of the circle is 2π x radius = 40π
Statement 1 is sufficient.
Statement 2: PR = 24 and QR = 32
Angles 24, 32, and 40 form a Pythagorean triplet. So, triangle PQR is a right-angled triangle, right-angled at angle R. Again, if angle PRQ is 90°, then the PQ must be the diameter since the angle in a semicircle is 90° (circle theorem)
So, diameter = 40 units, i.e. radius = 20 units. Therefore, the circumference of the circle is 2π x radius = 40π
Statement 2 is sufficient.
Therefore, the correct answer is D.
19 May 2020, 13:10
Kudos
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Statement 1: if the angle subtended at by a chord at the circumference is 90,
then that chord is the diameter
Statement 2: Three distinct no-colinear points will form a unique circle with a unique circumference,radius and area.We have 3 points that fit these criteria.
Sufficient
Answer is D
then that chord is the diameter
Statement 2: Three distinct no-colinear points will form a unique circle with a unique circumference,radius and area.We have 3 points that fit these criteria.
Sufficient
Answer is D
