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03 May 2020, 10:32
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B
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Difficulty:
65%
(hard)
Question Stats:
59% (02:39) correct
41%
(03:08)
wrong
based on 75
sessions
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Two identical circles, with centers O and O" and radii of 5 are tangent to PQ at points P and Q, respectively as well as to RS at points R and S, respectively as shown above. If RS = 24 cm, what it is the length of PQ?
A. 25 cm
B. 26 cm
C. 27 cm
D. 28 cm
E. 29 cm
Are You Up For the Challenge: 700 Level Questions
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03 May 2020, 15:42
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∠ORT = ∠O'ST = 90 {A tangent makes an angle of 90 degrees with the radius of a circle}
∠OTR = ∠O'TS {opposite angles}
∠ROT = ∠SO'T
Also, OR = O'S
BY ASA, Triangle ORT is congruent to triangle O'ST
Hence, RT = ST = 24/2= 12
\(OT=O'T = \sqrt{12^2+5^2} = 13\)
OO'=PQ = 13+13=26
∠OTR = ∠O'TS {opposite angles}
∠ROT = ∠SO'T
Also, OR = O'S
BY ASA, Triangle ORT is congruent to triangle O'ST
Hence, RT = ST = 24/2= 12
\(OT=O'T = \sqrt{12^2+5^2} = 13\)
OO'=PQ = 13+13=26
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03 May 2020, 22:52
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Bunuel
STep-by-step detailed explanation may be viewed in Video
Answer : Option B
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