Skip to content / Đến nội dung
ThichHocToan.com

Australian AMC 2011 - Senior Question 25

AMC AUSTRALIA · Australian AMC 2011 - Senior

Question 25

A cone has base diameter 1 unit and slant height 3 units. From a point $A$ halfway up the side of the cone, a string is passed twice around it to come to a point $B$ on the circumference of the base, directly below $A$. The string is then pulled until taut.

Question illustration

How far is it from $A$ to $B$ along this taut string?
  1. $\frac38(\sqrt{29}+\sqrt{53})$
  2. $\frac{3\sqrt7}{2}$
  3. $\frac{3\sqrt3}{2}$
  4. $\frac94$
  5. $\frac{3\sqrt{108}}8$