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2007 AMC 10B Problem 17

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2007 AMC 10B Problem 17AMC 10 Step by Step

Name: Date: September 13, 2026

Triangles: Area & Pythagorean · difficulty 3 of 5 · about 4 min · position P16-20

Point $P$ is inside equilateral $\triangle ABC$ . Points $Q$ , $R$ , and $S$ are the feet of the perpendiculars from $P$ to $\overline{AB}$ , $\overline{BC}$ , and $\overline{CA}$ , respectively. Given that $PQ=1$ , $PR=2$ , and $PS=3$ , what is $AB$ ?

A)
$4$
B)
$3\sqrt{3}$
C)
$6$
D)
$4\sqrt{3}$
E)
$9$

2007 AMC 10B Problem 17

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