ISEE Upper Level Quantitative : Circles
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Example Questions
Example Question #6 : How To Find The Length Of An Arc
Acute triangle 
(a)
(b)
It is impossible to determine which is greater from the information given
(a) is the greater quantity
(a) and (b) are equal
(b) is the greater quantity
(a) and (b) are equal
Examine the figure below, which shows 
By the Arc Addition Principle,
and
Consequently,
The two quantities are equal.
Example Question #51 : Circles
Which is the greater quantity?
(a) The degree measure of a 10-inch-long arc on a circle with radius 8 inches.
(b) The degree measure of a 12-inch-long arc on a circle with radius 10 inches.
It is impossible to tell from the information given.
(a) is greater.
(a) and (b) are equal.
(b) is greater.
(a) is greater.
(a) A circle with radius 8 inches has crircumference 
(b) A circle with radius 10 inches has crircumference 
(a) is the greater quantity.
Example Question #52 : Circles
Note: figure NOT drawn to scale
Refer to the above figure. Which is the greater quantity?
(a)
(b)
(b) is greater
(a) is greater
(It is impossible to tell from the information given
(a) and (b) are equal
(a) and (b) are equal
Since
the triangle is a right triangle with right angle 
Example Question #53 : Circles
Note: Figure NOT drawn to scale
Refer to the above figure. Which is the greater quantity?
(a)
(b) 90
It is impossible to tell from the information given
(a) is greater
(b) is greater
(a) and (b) are equal
(b) is greater
The measure of an arc intercepted by an inscribed angle of a circle is twice that of the angle. Therefore,
Example Question #184 : Geometry
Which is the greater quantity?
(a) Twice the degree measure of the central angle of Sector 1
(b) The degree measure of the central angle of Sector 2
(a) is greater
(a) and (b) are equal
It is impossible to tell from the information given
(b) is greater
(b) is greater
Example Question #1 : How To Find The Angle Of A Sector
Refer to the above figure. Which is the greater quantity?
(a)
(b) 55
(b) is greater
(a) and (b) are equal
(a) is greater
It is impossible to tell from the information given
(a) and (b) are equal
The measure of an inscribed angle of a circle is one-half that of the arc it intercepts. Therefore, 
Example Question #184 : Plane Geometry
The arc-length for the shaded sector is 
Remember that the angle for a sector or arc is found as a percentage of the total 
The circumference of a circle is found by:
For our data, this means:
Now we can solve for 
Cross multiply:
Divide both sides by 
Therefore, 
Example Question #7 : How To Find The Angle Of A Sector
The arc-length for the shaded sector is 
Remember that the angle for a sector or arc is found as a percentage of the total 
The circumference of a circle is found by:
For our data, this means:
Now we can solve for 
Cross multiply:
Divide both sides by 
Therefore, 
Example Question #8 : How To Find The Angle Of A Sector
The area of the shaded sector in circle O is 
Remember that the angle for a sector or arc is found as a percentage of the total 
The area of a circle is found by:
For our data, this means:
Now we can solve for 
Cross multiply:
Divide both sides by 
Therefore, 
Example Question #9 : How To Find The Angle Of A Sector
The area of the shaded sector in circle O is 
Remember that the angle for a sector or arc is found as a percentage of the total 
The area of a circle is found by:
For our data, this means:
Now we can solve for 
Cross multiply:
Divide both sides by 
Therefore, 
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