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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A rectangle is inscribed in a circle of radius r. If the rectangle is

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Retired Moderator V
Joined: 27 Oct 2017
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WE: General Management (Education)
Re: A rectangle is inscribed in a circle of radius r. If the rectangle is  [#permalink]

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It is one of the probable cases.

See my solution in earlier post, I have explained without using 30:60:90 triangle.

gmatbusters wrote:
Is this always the case? That the right triangles within a rectangle are always 30-60-90?

See the figure
Attachment:
IMG_20180518_083441.jpg

Is this always the case? That the right triangles within a rectangle are always 30-60-90?

Got it. Why is it 30-60-90 in this case? (other than looking at the answers)?[/quote]

Posted from my mobile device
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Veritas Prep GMAT Instructor V
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Re: A rectangle is inscribed in a circle of radius r. If the rectangle is  [#permalink]

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gmatbusters wrote:
Is this always the case? That the right triangles within a rectangle are always 30-60-90?

See the figure
Attachment:
IMG_20180518_083441.jpg

Is this always the case? That the right triangles within a rectangle are always 30-60-90?

Got it. Why is it 30-60-90 in this case? (other than looking at the answers)?[/quote]

The angles can take many values. Look at the question: which of the following could be the perimeter ...

The reason we think of 30-60-90 triangle is that we know sides of only 45-45-90 and 30-60-90 triangles. GMAT will not ask us to find the sides of 10-80-90 triangle. Since it is not a square, we should try out the 30-60-90 triangle.
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Karishma
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Re: A rectangle is inscribed in a circle of radius r. If the rectangle is  [#permalink]

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Can someone please explain why you can multiply or divide each item in an equation (i.e. a+b=c -----> a/2 + b/2 = c/2) but you cannot square root each item in an equation (i.e. a^2 + b^2 = c^2 ---/--> a+b=c)?
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Re: A rectangle is inscribed in a circle of radius r. If the rectangle is  [#permalink]

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Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10797
Location: Pune, India
A rectangle is inscribed in a circle of radius r. If the rectangle is  [#permalink]

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1
crazi4ib wrote:

The operation of squaring is not the same as that of multiplication/division.

Given: a + b = c

Squaring both sides, you get,

$$(a + b)^2 = c^2$$

$$a^2 + b^2 + 2ab = c^2$$

Take an example, $$3^2 = 9$$, $$4^2 = 16$$.
The sum of these two is 9 + 16 = 25. It is not the same as $$(3 + 4)^2 = 7^2 = 49$$.
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Re: A rectangle is inscribed in a circle of radius r. If the rectangle is  [#permalink]

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_________________ Re: A rectangle is inscribed in a circle of radius r. If the rectangle is   [#permalink] 21 Jun 2020, 13:21

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