20

Part of 2014 BMT Spring

Problems(2)

2014 BMT Team 20 integral

Source:

A certain type of Bessel function has the form

I(x) = \frac{1}{\pi} \int_0^{\pi}e^{x \cos \theta} d\theta

x

\int_0^{\infty} x I(2x) e^{-x^2}dx

algebracalculusintegration

min circle containing 3 concurrent equal circles 2014 BMT Individual 20

Source:

Suppose three circles of radius

5

intersect at a common point. If the three (other) pairwise intersections between the circles form a triangle of area

8

, find the radius of the smallest possible circle containing all three circles.

geometrycirclesequal circles