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# If the line segment AB is one of the sides of a regular polygon inscri

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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
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If the line segment AB is one of the sides of a regular polygon inscri  [#permalink]

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27 Feb 2019, 18:48
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Difficulty:

55% (hard)

Question Stats:

55% (01:47) correct 45% (01:40) wrong based on 22 sessions

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GMATH practice exercise (Quant Class 15)

If the line segment AB is one of the sides of a regular polygon inscribed in the given circle with center O, how many sides does this polygon have?

(1) $$\,\alpha = {30^ \circ }$$.
(2) The circumference of the circle is equal to$$\,4\pi \,$$.

Attachment:

27-Feb19-8r.gif [ 8.99 KiB | Viewed 333 times ]

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: If the line segment AB is one of the sides of a regular polygon inscri  [#permalink]

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28 Feb 2019, 07:22
fskilnik wrote:
GMATH practice exercise (Quant Class 15)

If the line segment AB is one of the sides of a regular polygon inscribed in the given circle with center O, how many sides does this polygon have?

(1) $$\,\alpha = {30^ \circ }$$.
(2) The circumference of the circle is equal to$$\,4\pi \,$$.

$${\rm{regular}}\,\,N{\rm{ - polygon}}\,\,\left( {N \ge 3\,\,{\mathop{\rm int}} } \right)$$

$$? = N$$

$$\left( 1 \right)\,\,\alpha = {30^ \circ }\,\,\,\, \Rightarrow \,\,\,\angle AOB = {60^ \circ }\,\,\,\left( {{\rm{central}}\,\,{\rm{angle}}} \right)\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{regularity}}} \,\,\,\,\,? = {{{{360}^ \circ }} \over {{{60}^ \circ }}} = 6\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$

$$\left( 2 \right)\,\,2\pi r = 4\pi \,\,\, \Rightarrow \,\,\,r = 2\,\,\,:\,\,\left( {{\rm{images}}} \right)\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\alpha = {30^ \circ }\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{regularity}}} \,\,\,\,\,\,? = {{{{360}^ \circ }} \over {{{60}^ \circ }}} = 6\,\,\,\,\left( {{\rm{regular}}\,\,{\rm{hexagon}}} \right) \hfill \cr \,{\rm{Take}}\,\,\alpha = {60^ \circ }\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{regularity}}} \,\,\,\,\,\,? = {{{{360}^ \circ }} \over {{{120}^ \circ }}} = 3\,\,\,\,\left( {{\rm{equilateral}}\,\,{\rm{triangle}}} \right) \hfill \cr} \right.$$

The correct answer is (A).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Re: If the line segment AB is one of the sides of a regular polygon inscri   [#permalink] 28 Feb 2019, 07:22
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# If the line segment AB is one of the sides of a regular polygon inscri

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