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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?

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=r-2

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(r-2)+sq(6) which gives r=10

now area=pi*r*r=100*pi

Hope it helps.
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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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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 :

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.

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°."

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°."

Check the diagram below:

Angle ABC is inscribed in semicircle, thus angle B is 90 degrees.

It's the same as the following property: a right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle.

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.

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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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 .

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?

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.

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.
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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?

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“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...

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