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Math: Circles

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sandeep800
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Re: Math: Circles [#permalink] New post  20 Sep 2010, 10:05
hey thanx a lot bunuel for these circles!!as i needed bit more material for concepts...
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mission2009
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Re: Math: Circles [#permalink] New post  07 Oct 2010, 20:50
Thanks for the concepts..
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Sarang
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Re: Math: Circles [#permalink] New post  11 Nov 2010, 15:49
The post is just awesome....!! Thanks once again Bunuel...!
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Re: Math: Circles [#permalink] New post  12 Feb 2011, 21:31
Just came across this, great stuff!
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avellanj2
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Re: Math: Circles [#permalink] New post  27 Apr 2011, 18:51
Bunuel,

What angle would be the angle opposite to alpha? I am a bit confused.
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Re: Math: Circles [#permalink] New post  26 Jun 2011, 11:55
Hi all!
Help me please with one task concerning inscribed triangles and circles :roll:
here it is:
Circle A,centre X. XB is the radius. There is a chord AC which intersects XB. D is the point of intersection between XB and AC. BD=2;AC=12;XDA= 90 degrees. What is the circles area?
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Asher
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Re: Math: Circles [#permalink] New post  23 Jul 2011, 21:40
Thanks Bunuel.. love your explanations... very simple, clear and easy to comprehend.. Kudos
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Jdam
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Re: Math: Circles [#permalink] New post  13 Nov 2011, 23:30
This is probably my worst area in all of gmat. This helps! thanks!
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Re: Math: Circles [#permalink] New post  20 Nov 2011, 06:43
Wow.... I've just started and U've made me fall in love with Circles all over... Thank you...
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Re: Math: Circles [#permalink] New post  16 Aug 2012, 11:42
Bunuel wrote:
chauhan2011 wrote:
• If you know the length of the minor arc and radius, the inscribed angle is: 90L/nr

Please correct me if i am wrong but i think the formula should be : 180L/nr


If you know the length \(L\) of the minor arc and radius, the inscribed angle is: \(Inscribed \ Angle=\frac{90L}{\pi{r}}\).

The way to derive the above formula:

LengAngle=\frac{180L}{\pi{r}}[/m] --> \(Inscribed \ Angle=\frac{90L}{\pi{r}}\).

Hope it helps.



Hello, quick conceptual question

The circle represented by the equation x^ 2 + y^ 2 =1 is centered at the origin and has the radius of r= √1 = 1

What is the correlation between the function and the radius for a circle?
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goutamread
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Re: Math: Circles [#permalink] New post  28 Oct 2012, 11:52
A secant\chord (except diameter) to a circle divides circle into two region - minor and major. The area of minor region can be calculate by determining area of minor sector minus triangle. Also the direct formula to calculate minor region area is :

\(A=\frac{1}{2}r^2*(\frac{pi*center angle}{180}-sin(\frac{pi*center angle}{180}))\)
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naiduashwini
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Re: Math: Circles [#permalink] New post  20 Jul 2013, 23:16
Tangent-Secant


Image

Should one of the lines be tangent to the circle, point A will coincide with point D, and the theorem still applies:

PA*PD=PC*PB=Constant

PA^2=PC*PB=Constant - This becomes the theorem we know as the theorem of secant-tangent theorem.


Does this hold true if CB was the diameter of the circle?
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Re: Math: Circles [#permalink] New post  21 Jul 2013, 01:55
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naiduashwini wrote:
Tangent-Secant


Image

Should one of the lines be tangent to the circle, point A will coincide with point D, and the theorem still applies:

PA*PD=PC*PB=Constant

PA^2=PC*PB=Constant - This becomes the theorem we know as the theorem of secant-tangent theorem.


Does this hold true if CB was the diameter of the circle?

____________
Yes, it does.
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Re: Math: Circles [#permalink] New post  01 Dec 2013, 05:04
Can somebody explain the properties of a cyclic quadrilateral. Also, do the same properties hold good for a cyclic quadrilateral inscribed in a semicircle with one of its sides being the diameter of that semicircle.
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Re: Math: Circles [#permalink] New post  11 Dec 2013, 21:00
Thanks so much!!

Quick question - under the "Semicircles" section, could you clarify or show a picture of what this means? I don't understand how it would always be true.

"• The angle inscribed in a semicircle is always 90°."
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Re: Math: Circles [#permalink] New post  12 May 2014, 12:05
Bunuel, first of all thanks for another amazing post.

Wanted to check, there are a few concepts in this thread like secant, chord, point theorem etc. Are they tested in GMAT? And i have same question with your other quant concept threads.
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Re: Math: Circles [#permalink] New post  13 May 2014, 00:57
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gaurav1418z wrote:
Bunuel, first of all thanks for another amazing post.

Wanted to check, there are a few concepts in this thread like secant, chord, point theorem etc. Are they tested in GMAT? And i have same question with your other quant concept threads.


Some aspects of this properties definitely could be helpful when solving GMAT questions.
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Re: Math: Circles [#permalink] New post  05 Mar 2015, 14:31
Hi Brnuel ,

Would you please help me with this "easy " questions.

Triangle ABC is inscribed in a circle, such that AC is a diameter
of the circle (see figure). If AB has a length of 8 and BChas a
length of 15, what is the circumference of the circle?

Aren't we supposed to - after getting AC= 17 ( which is the diameter) to calculate the circumference as 2 π R .

Is not the r supposed to be 17/2 ?. Thanks.
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Re: Math: Circles [#permalink] New post  17 May 2015, 02:38
Excellent work. All the important things in just one post.
Power of point theorem is vague to me. How do we know that the product of two point of intersections is constant? Could someone explain please?

Thanks
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prasadcp
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Re: Math: Circles [#permalink] New post  04 Aug 2015, 09:58
Bunnel - on posts for triangle and circle i found the following- which one is correct ?

For a given perimeter equilateral triangle has the largest area.
A circle is the shape with the largest area for a given length of perimeter


Thanks
Prasad

Bunuel wrote:
gaurav1418z wrote:
Bunuel, first of all thanks for another amazing post.

Wanted to check, there are a few concepts in this thread like secant, chord, point theorem etc. Are they tested in GMAT? And i have same question with your other quant concept threads.


Some aspects of this properties definitely could be helpful when solving GMAT questions.
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Re: Math: Circles [#permalink]
04 Aug 2015, 09:58
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