Track / Stage 4 / 49 of 340 #309 of 2000

Problem 309

AMC 12 late, AIME early

Geometry Difficulty 4.5 Find the answer

3. For an equilateral $\triangle ABC$ with side length $1$ , $P$ is a point on side $AB$ . $PQ \perp BC, \quad QR \perp AC, \quad RS \perp AB$ (where $Q, R, S$ are the feet of the perpendiculars). If $SP=\frac{1}{4}$ , then $AP=$

Your answer

Official solution

3. $\frac{1}{9}$ or $\frac{5}{9}$ ,

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.