Difference between revisions of "FidgetBoss 4000's 2019 Mock AMC 12B Problems/Problem 2"
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==See also== | ==See also== | ||
| − | {{AMC12 box|year=2019|ab=B|before=[[FidgetBoss 4000's 2019 Mock AMC 12B Problems/Problem 1|Problem 1]]|after=[[FidgetBoss 4000's 2019 Mock AMC 12B Problems/Problem 3|Problem 3]]}} | + | {{AMC12 box|year=FidgetBoss 4000's 2019 Mock|ab=B|before=[[FidgetBoss 4000's 2019 Mock AMC 12B Problems/Problem 1|Problem 1]]|after=[[FidgetBoss 4000's 2019 Mock AMC 12B Problems/Problem 3|Problem 3]]}} |
[[Category:Introductory Geometry Problems]] | [[Category:Introductory Geometry Problems]] | ||
{{FidgetBoss Notice}} | {{FidgetBoss Notice}} | ||
Latest revision as of 15:26, 19 November 2020
Problem
(fidgetboss_4000) In the diagram below, 
is an isosceles right triangle with a right angle at 
and with a hypotenuse of 
units. Find the greatest integer less than or equal to the value of the radius of the quarter circle inscribed inside 
.
Solution
The quarter circle is centered at and just touches the hypotenuse at the midpoint of the hypotenuse due to symmetry in an isosceles right triangle. The value of its radius is equal to the distance between and the midpoint of the hypotenuse, and it is well known that this is half the length of the hypotenuse, or 
. The greatest integer less than or equal to 
is 
, thus we pick answer 
.
See also
| FidgetBoss 4000's 2019 Mock AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 1 |
Followed by Problem 3 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by FidgetBoss 4000's Mock American Mathematics Competitions. 
