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Circle O has a diameter AB of length 10 cm. Two points P and Q lie on
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11 Mar 2022, 23:00
11 Mar 2022, 23:00
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Circle O has a diameter AB of length 10 cm. Two points P and Q lie on the circle such that the length of chord PB is 6 cm, and the length of chord AP is twice that of chord AQ. What is the length (in cm) of chord QB?
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\(\sqrt{84}\) or \(9.16\)
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: Circle O has a diameter AB of length 10 cm. Two points P and Q lie on
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24 Mar 2022, 21:56
24 Mar 2022, 21:56
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KarunMendiratta wrote:
Circle O has a diameter AB of length 10 cm. Two points P and Q lie on the circle such that the length of chord PB is 6 cm, and the length of chord AP is twice that of chord AQ. What is the length (in cm) of chord QB?
Show: ::
\(\sqrt{84}\) or \(9.16\)
Refer to the figure below.
Use Thale's Theorem: if A, B, and P are distinct points on a circle where the line AB is a diameter, the angle APB is a right angle.
In △APB;
\(AB^2 = AP^2 + PB^2\)
\(10^2 = (2x)^2 + 6^2\)
\(2x = 8\)
\(x = 4\)
i.e. AQ = 4cm
Now, In △AQB;
\(AB^2 = AQ^2 + QB^2\)
\(10^2 = (x)^2 + QB^2\)
\(10^2 = 4^2 + QB^2\)
\(QB^2 = 84\)
\(QB = \sqrt{84}\)
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gmatclubot
Re: Circle O has a diameter AB of length 10 cm. Two points P and Q lie on [#permalink]
24 Mar 2022, 21:56
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