This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 4

2014-2015 SDML (High School), 2
Tags: 2014-15 SDML Round 1 , SDML High School , SDMO Middle School
A circle of radius $5$ is inscribed in an isosceles right triangle, $ABC$. The length of the hypotenuse of $ABC$ can be expressed as $a+a\sqrt{2}$ for some $a$. What is $a$?

2008 SDMO (Middle School), 3
Tags: geometry , NEEDS DIAGRAM , SDMO Middle School , 2008 SDMO
In the diagram, $AD:DB=1:1$, $BE:EC=1:2$, and $CF:FA=1:3$. If the area of triangle $ABC$ is $120$, then find the area of triangle $DEF$. (will insert image here later)

2012-2013 SDML (Middle School), 2
Tags: 2012-13 SDML Round 1 , SDMO Middle School
Each of Marta's fish has exactly $3$ fins or $4$ fins. Marta's $13$ fish have a total of $44$ fins. How many $3$-finned fish does Marta have? $\text{(A) }5\qquad\text{(B) }6\qquad\text{(C) }7\qquad\text{(D) }8\qquad\text{(E) }9$

2014-2015 SDML (Middle School), 5
Tags: 2014-15 SDML Round 1 , SDML High School , SDMO Middle School
A circle of radius $5$ is inscribed in an isosceles right triangle, $ABC$. The length of the hypotenuse of $ABC$ can be expressed as $a+a\sqrt{2}$ for some $a$. What is $a$?