Feb 16

Welcome back.

Today, we'll look at

1. the relational properties of lines and circles, as in tangents and secants. and time permits, start to go over

2. the relational properties between circles and circles.

Assignments

(AMC10 2008) A round table has radius 4. Six rectangular place mats are placed on the table. Each place mat has width 1 and length x. They are positioned so that each mat has two corners on the edge of the table, these two corners being end points of the same side of length x. Further, the mats are positioned so that the inner corners each touch an inner corner of an inner corner of an adjacent mat. Find x.

(AIME 2005) Six congruent circles from a ring with each circle externally tangent to the two circles adjacent to it. All six circles are internally tangent to a circle C with radius 30. Let K be the area of the region inside C and outside all of the six circles in the ring. Find K.