csat-suneung 2020 Q17

csat-suneung · South-Korea · csat__math-science 4 marks Conic sections Optimization on Conics

In a plane, there is an equilateral triangle ABC with side length 10. For a point P satisfying $\overline { \mathrm { PB } } - \overline { \mathrm { PC } } = 2$, when the length of segment PA is minimized, what is the area of triangle PBC? [4 points]
(1) $20 \sqrt { 3 }$
(2) $21 \sqrt { 3 }$
(3) $22 \sqrt { 3 }$
(4) $23 \sqrt { 3 }$
(5) $24 \sqrt { 3 }$

In a plane, there is an equilateral triangle ABC with side length 10. For a point P satisfying $\overline { \mathrm { PB } } - \overline { \mathrm { PC } } = 2$, when the length of segment PA is minimized, what is the area of triangle PBC? [4 points]\\
(1) $20 \sqrt { 3 }$\\
(2) $21 \sqrt { 3 }$\\
(3) $22 \sqrt { 3 }$\\
(4) $23 \sqrt { 3 }$\\
(5) $24 \sqrt { 3 }$

Paper Questions

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