Throughout the year, the MAT Department hosts a number of informal events meant to help build and sustain our mathematical sciences community here at DePaul. These events provide an opportunity to meet with fellow MAT students, at both undergraduate and graduate levels, as well as MAT faculty members in a relaxed setting.

We will have five teas during the spring quarter:

• Friday, 4/4 at 1:30-2:45 pm
• Friday, 4/25 at 1:30-2:45 pm
• Friday, 5/9 at 1:15-2:45 pm
• Friday, 5/16 at 1:30-2:45 pm 
• Friday, 5/30 at 1:30-2:45 pm 

These community hours will take place in the MAT Department office suite (on the 5th floor of SAC, roughly SAC 546). Light refreshments, such as coffee, tea, and cookies, will be served. We hope that you can join us.

Two circles are concentric. A chord c units long cuts across the larger, tangent to the smaller. What is the area of the shaded region in terms of c?

Solution: [From MT Nov 1991]

Let the radii of the smaller and larger circles be r and R respectively, so the area we seek is given by ℼR² – ℼr².  Now, let A be the center of both circles, let point B be the point of tangency of the chord, and D be the point of intersection with the larger circle, as indicated.  Now, because triangle ABD is right, we have r² + (c/2)² = R², so that R² – r² = (c/2)².  The shaded area is then equal to ℼc²/4.