Difference between revisions of "2022 AIME II Problems/Problem 7"

Revision as of 07:55, 19 February 2022

Problem

A circle with radius $6$ is externally tangent to a circle with radius $24$ . Find the area of the triangular region bounded by the three common tangent lines of these two circles.

Solution 1

$[asy] //Created by isabelchen draw(circle((0,0),24)); draw(circle((30,0),6)); draw((72/5, 96/5) -- (40,0)); draw((72/5, -96/5) -- (40,0)); draw((24, 12) -- (24, -12)); draw((0, 0) -- (40, 0)); draw((72/5, 96/5) -- (0,0)); draw((168/5, 24/5) -- (30,0)); draw((54/5, 72/5) -- (30,0)); dot((72/5, 96/5)); label("$A$",(72/5, 96/5),NE); dot((168/5, 24/5)); label("$B$",(168/5, 24/5),NE); dot((24,0)); label("$C$",(24,0),NW); dot((40, 0)); label("$D$",(40, 0),NE); dot((24, 12)); label("$E$",(24, 12),NE); dot((0, 0)); label("$O_1$",(0, 0),S); dot((30, 0)); label("$O_2$",(30, 1/3),S); [/asy]$

To be continued......

~isabelchen

Video Solution (Mathematical Dexterity)

https://www.youtube.com/watch?v=7NGkVu0kE08

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Difference between revisions of "2022 AIME II Problems/Problem 7"

Revision as of 07:55, 19 February 2022

Contents

Problem

Solution 1

Video Solution (Mathematical Dexterity)

See Also

@@ Line 17: / Line 17: @@
 draw((168/5, 24/5) -- (30,0));
 draw((54/5, 72/5) -- (30,0));
+dot((72/5, 96/5));
+label("$A$",(72/5, 96/5),NE);
+dot((168/5, 24/5));
+label("$B$",(168/5, 24/5),NE);
+dot((24,0));
+label("$C$",(24,0),NW);
+dot((40, 0));
+label("$D$",(40, 0),NE);
+dot((24, 12));
+label("$E$",(24, 12),NE);
+dot((0, 0));
+label("$O_1$",(0, 0),S);
+dot((30, 0));
+label("$O_2$",(30, 1/3),S);
 </asy>