Skip to main content
OlympiadHQ

Browse · harp

Print

imc

geometry intermediate

Problem

Seven cookies of radius inch are cut from a circle of cookie dough, as shown. Neighboring cookies are tangent, and all except the center cookie are tangent to the edge of the dough. The leftover scrap is reshaped to form another cookie of the same thickness. What is the radius in inches of the scrap cookie?
problem
(A)
(B)
(C)
(D)
Solution
The big cookie has radius , since the center of the center cookie is the same as that of the large cookie. The difference in areas of the big cookie and the seven small ones is . The scrap cookie has this area, so its radius must be .
Final answer
A