Difference between revisions of "2020 AMC 12A Problems/Problem 24"
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| − | =Problem 24= | + | ==Problem 24== |
Suppose that <math>\triangle{ABC}</math> is an equilateral triangle of side length <math>s</math>, with the property that there is a unique point <math>P</math> inside the triangle such that <math>AP=1</math>, <math>BP=\sqrt{3}</math>, and <math>CP=2</math>. What is <math>s</math>? | Suppose that <math>\triangle{ABC}</math> is an equilateral triangle of side length <math>s</math>, with the property that there is a unique point <math>P</math> inside the triangle such that <math>AP=1</math>, <math>BP=\sqrt{3}</math>, and <math>CP=2</math>. What is <math>s</math>? | ||
<math>\textbf{(A) } 1+\sqrt{2} \qquad \textbf{(B) } \sqrt{7} \qquad \textbf{(C) } \frac{8}{3} \qquad \textbf{(D) } \sqrt{5+\sqrt{5}} \qquad \textbf{(E) } 2\sqrt{2}</math> | <math>\textbf{(A) } 1+\sqrt{2} \qquad \textbf{(B) } \sqrt{7} \qquad \textbf{(C) } \frac{8}{3} \qquad \textbf{(D) } \sqrt{5+\sqrt{5}} \qquad \textbf{(E) } 2\sqrt{2}</math> | ||
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| + | ==Solution 1== | ||
Revision as of 18:17, 1 February 2020
Problem 24
Suppose that 
is an equilateral triangle of side length 
, with the property that there is a unique point 
inside the triangle such that 
, 
, and 
. What is ?
