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# What is the value of b, in the inscribed triangle above?

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Math Expert
Joined: 02 Sep 2009
Posts: 55662
What is the value of b, in the inscribed triangle above?  [#permalink]

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12 Sep 2018, 00:44
00:00

Difficulty:

55% (hard)

Question Stats:

70% (02:13) correct 30% (00:51) wrong based on 13 sessions

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What is the value of b, in the inscribed triangle above?

(1) The area of triangle PQR is 80.
(2) c/b = b/a

Attachment:

image012 (1).jpg [ 6.32 KiB | Viewed 273 times ]

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Re: What is the value of b, in the inscribed triangle above?  [#permalink]

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12 Sep 2018, 04:57
Bunuel wrote:

What is the value of b, in the inscribed triangle above?

(1) The area of triangle PQR is 80.
(2) c/b = b/a

Attachment:
image012 (1).jpg

Question : What is the value of b, in the inscribed triangle above?

As per the given figure, Triangle PQR is a right triangle with right angle t Q (Property: Every angle on circumference in a semicircle is a right angle)
Let the dotted line be QS
now triangle PQR, PQS and QRS are all similar triangles

Statement 1: The area of triangle PQR is 80

Radius of the circle is unknown hence

NOT SUFFICIENT

Statement 2: c/b = b/a

By the property of similar triangle we already know this hence

NOT SUFFICIENT

Combining the two statements

Second statement is redundant hence combining doesn't give us any further information hence

NOT SUFFICIENT

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Re: What is the value of b, in the inscribed triangle above?   [#permalink] 12 Sep 2018, 04:57
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