Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 16 Jan 2011
Posts: 107

Re: Math: Circles [#permalink]
Show Tags
26 Jun 2011, 11:55
Hi all! Help me please with one task concerning inscribed triangles and circles 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?



Manager
Joined: 29 Jun 2011
Posts: 70

Re: Math: Circles [#permalink]
Show Tags
01 Jul 2011, 13:07
Galiya wrote: Hi all! Help me please with one task concerning inscribed triangles and circles 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? By basic property of the circle, the radius bisects the chord AC . ie CD equals AC/2 ie 6 now see, radius XB=XD+BD ie r=XD+2 ie XD=r2 now concerning Triangle XCD, angle XDC= XDA =90 so pythagorean theorem is applicable so, sq(XC)=sq(DC)+sq(XD) plug in values you get sq(r)=sq(r2)+sq(6) which gives r=10 now area=pi*r*r=100*pi Hope it helps.
_________________
It matters not how strait the gate, How charged with punishments the scroll, I am the master of my fate : I am the captain of my soul. ~ William Ernest Henley



Manager
Joined: 06 Apr 2011
Posts: 70
Location: India

Re: Math: Circles [#permalink]
Show Tags
23 Jul 2011, 21:40
Thanks Bunuel.. love your explanations... very simple, clear and easy to comprehend.. Kudos
_________________
Regards, Asher



Manager
Joined: 21 Nov 2010
Posts: 112

Re: Math: Circles [#permalink]
Show Tags
13 Nov 2011, 23:30
This is probably my worst area in all of gmat. This helps! thanks!



Intern
Joined: 27 Jun 2011
Posts: 17
Location: Chennai
WE 1: 2.10

Re: Math: Circles [#permalink]
Show Tags
20 Nov 2011, 06:43
Wow.... I've just started and U've made me fall in love with Circles all over... Thank you...



Senior Manager
Joined: 15 May 2011
Posts: 273
Location: Costa Rica
Concentration: Healthcare, International Business
GMAT 1: 710 Q42 V45 GMAT 2: 740 Q48 V42
GPA: 3.3
WE: Research (Consulting)

Re: Math: Circles [#permalink]
Show Tags
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?
_________________
How to improve your RC score, pls Kudo if helpful! http://gmatclub.com/forum/howtoimprovemyrcaccuracy117195.html Work experience (as of June 2012) 2.5 yrs (Currently employed)  Mckinsey & Co. (US Healthcare Analyst) 2 yrs  Advertising industry (client servicing)



Intern
Status: Active
Joined: 30 Jun 2012
Posts: 37
Location: India

Re: Math: Circles [#permalink]
Show Tags
28 Oct 2012, 11:52
2
This post received KUDOS
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 : \(A=\frac{1}{2}r^2*(\frac{pi*center angle}{180}sin(\frac{pi*center angle}{180}))\)
_________________
Thanks and Regards!
P.S. +Kudos Please! in case you like my post.



Math Expert
Joined: 02 Sep 2009
Posts: 44298

Re: Math: Circles [#permalink]
Show Tags
11 Jul 2013, 00:06



Intern
Joined: 15 May 2012
Posts: 1
Location: India
Concentration: Healthcare
GMAT Date: 08072012
GPA: 3.98
WE: Science (Pharmaceuticals and Biotech)

Re: Math: Circles [#permalink]
Show Tags
20 Jul 2013, 23:16
TangentSecant
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 secanttangent theorem.
Does this hold true if CB was the diameter of the circle?



Math Expert
Joined: 02 Sep 2009
Posts: 44298

Re: Math: Circles [#permalink]
Show Tags
21 Jul 2013, 01:55



Manager
Joined: 07 May 2013
Posts: 104

Re: Math: Circles [#permalink]
Show Tags
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.



Current Student
Joined: 26 May 2012
Posts: 47
Concentration: Marketing, Statistics

Re: Math: Circles [#permalink]
Show Tags
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°."



Math Expert
Joined: 02 Sep 2009
Posts: 44298

Re: Math: Circles [#permalink]
Show Tags
12 Dec 2013, 02:52



Intern
Joined: 25 Jan 2014
Posts: 46
Concentration: Strategy, International Business
GMAT 1: 600 Q44 V29 GMAT 2: 710 Q48 V38
GPA: 3.35
WE: Analyst (Computer Software)

Re: Math: Circles [#permalink]
Show Tags
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.



Math Expert
Joined: 02 Sep 2009
Posts: 44298

Re: Math: Circles [#permalink]
Show Tags
13 May 2014, 00:57



Intern
Joined: 15 Nov 2014
Posts: 21

Re: Math: Circles [#permalink]
Show Tags
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.



Manager
Joined: 16 Jan 2013
Posts: 102
Location: Bangladesh
GMAT 1: 490 Q41 V18 GMAT 2: 610 Q45 V28
GPA: 2.75

Re: Math: Circles [#permalink]
Show Tags
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
_________________
Heading towards perfection>>



Intern
Joined: 08 Jun 2015
Posts: 3

Re: Math: Circles [#permalink]
Show Tags
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.



Math Expert
Joined: 02 Sep 2009
Posts: 44298

Re: Math: Circles [#permalink]
Show Tags
16 Aug 2015, 10:03
prasadcp wrote: 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. Both. The first property is for triangles only. Meaning that for a given perimeter of a triangle, equilateral triangle has the largest area.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 23 Sep 2015
Posts: 44

Math: Circles [#permalink]
Show Tags
24 Jan 2016, 00:35
the Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle.
Image
• An inscribed angle is exactly half the corresponding central angle. Hence, all inscribed angles that subtend the same arc are equal. Angles inscribed on the arc are supplementary. In particular, every inscribed angle that subtends a diameter is a right angle (since the central angle is 180 degrees).
in the image there's an angle alpha which is outside the circle which could be found out easily if we are given its supplementary angle, hey bunuel what i cant understand is the relation between the central angle and the inscribed angle can you please help me out?
i cant get the image pasted here :/







Go to page
Previous
1 2 3
Next
[ 43 posts ]



