richachampion wrote:If a circle passes through points (1,2), (2,5), and (5,4), what is the diameter of the circle?
√18
√20
√22
√26
√30
Plot and connect (1,2), (2,5) and (5,4):
Notice that the angle formed by the three points is a RIGHT ANGLE.
Slope formed by (1,2) and (2,5) = (5-2)/(2-1) = 3.
Slope formed by (2,5) and (5,4) = (4-5)/(5-2) = -1/3.
Since the slopes are negative reciprocals, the two line segments are perpendicular and thus form a right angle.
This right angle constitutes an INSCRIBED ANGLE in the circle:
An inscribed right angle in a circle intercepts the DIAMETER:
To determine the length of the diameter, draw a right triangle, as follows:
In the resulting right triange:
4² + 2² = d²
20 = d²
d = √20.
The correct answer is
B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
