2

Part of 2013 BMT Spring

Problems(4)

BMT 2013 Spring - Geometry 2

Source:

Two rays start from a common point and have an angle of

60

degrees. Circle

C

is drawn with radius

42

such that it is tangent to the two rays. Find the radius of the circle that has radius smaller than circle

C

and is also tangent to

C

and the two rays.

2013 BMT Team 2

Source:

Find the sum of all positive integers

N

s =\sqrt[3]{2 + \sqrt{N}} + \sqrt[3]{2 - \sqrt{N}}

is also a positive integer

BMT 2013 Spring - Analysis 2

Source:

P

is given on the curve

x^4+y^4=1

. Find the maximum distance from the point

P

algebrageometryinequalities

4 semicircles in a circle 2013 BMT Individual 3

Source:

S-Corporation designs its logo by linking together

4

semicircles along the diameter of a unit circle. Find the perimeter of the shaded portion of the logo. https://cdn.artofproblemsolving.com/attachments/8/6/f0eabd46f5f3a5806d49012b2f871a453b9e7f.png

semicirclesemicirclesgeometry