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In the figure shown below,
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15 Jun 2021, 08:01
15 Jun 2021, 08:01
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In the figure shown below, the triangle PQR is inscribed in a semicircle. If the length of line segment PQ is 4 and the length of line segment QR is 3, what is the length of arc PQR?
(A) 3π
(B) 5π
(C) 7π/2
(D) 25π/2
(E) 5π/2
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Joined: 10 Apr 2015
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Re: In the figure shown below,
[#permalink]
15 Jun 2021, 09:43
15 Jun 2021, 09:43
1
Carcass wrote:
In the figure shown below, the triangle PQR is inscribed in a semicircle. If the length of line segment PQ is 4 and the length of line segment QR is 3, what is the length of arc PQR?
(A) 3π
(B) 5π
(C) 7π/2
(D) 25π/2
(E) 5π/2
Since the figure is a semicircle, we know that PR is the diameter of the circle
If PR is the diameter of the circle, then ∠Q is an inscribed angle "holding" (aka containing) the diameter.
One of our circle properties tells us that ∠Q must equal 90° (see video below for more on this)
This means ∆PQR is a RIGHT triangle, and its legs have lengths 3 and 4.
We can EITHER apply the Pythagorean Theorem to determine the length of the hypotenuse OR we can recognize that lengths 3 and 4 are parts of a "Pythagorean triplet" 3-4-5
Either way, we can determine that PR has length 5
What is the length of arc PQR?
Arc PQR is a half of the circle's circumference
Formula: circumference = (diameter)(π)
= (5)(π)
So, the length of arc PQR = (1/2)(5)(π) = 5π/2
Answer: E
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Re: In the figure shown below,
[#permalink]
07 Jul 2024, 11:24
07 Jul 2024, 11:24
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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