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Difference between revisions of "2022 MMATHS Individual Round Problems/Problem 2"

(Created page with "==Problem== Triangle <math>ABC</math> has <math>AB = 3, BC = 4,</math> and <math>CA = 5</math>. Points <math>D, E, F, G, H, </math> and <math>I</math> are the reflections of...")
 
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Triangle <math>ABC</math> has <math>AB = 3, BC = 4,</math> and <math>CA = 5</math>. Points <math>D, E, F, G, H, </math> and <math>I</math> are the reflections of <math>A</math> over <math>B</math>, <math>B</math> over <math>A</math>, <math>B</math> over <math>C</math>, <math>C</math> over <math>B</math>, <math>C</math> over <math>A</math>, and <math>A</math> over <math>C</math>, respectively. Find the area of hexagon <math>EFIDGH</math>.
 
Triangle <math>ABC</math> has <math>AB = 3, BC = 4,</math> and <math>CA = 5</math>. Points <math>D, E, F, G, H, </math> and <math>I</math> are the reflections of <math>A</math> over <math>B</math>, <math>B</math> over <math>A</math>, <math>B</math> over <math>C</math>, <math>C</math> over <math>B</math>, <math>C</math> over <math>A</math>, and <math>A</math> over <math>C</math>, respectively. Find the area of hexagon <math>EFIDGH</math>.
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==Solution 1==

Revision as of 20:11, 18 December 2022

Problem

Triangle $ABC$ has $AB = 3, BC = 4,$ and $CA = 5$. Points $D, E, F, G, H,$ and $I$ are the reflections of $A$ over $B$, $B$ over $A$, $B$ over $C$, $C$ over $B$, $C$ over $A$, and $A$ over $C$, respectively. Find the area of hexagon $EFIDGH$.

Solution 1

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