2025 AIME II Problems/Problem 1
Problem
Six points 
and 
lie in a straight line in that order. Suppose that 
is a point not on the line and that 
and 
Find the area of 
Solution 1
A=(0,0);
label("$A$", A, S);
B=(1.5,0);
label("$B$", B, S);
C=(2.9,0);
label("$C$", C, S);
D=(4.2,0);
label("$D$", D, S);
E=(5.3,0);
label("$E$", E, S);
F=(6.5,0);
label("$F$", F, S);
G=(3.7,3);
label("$G$", G, N);
draw(A--B--C--D--E--F);
draw(C--G--D);
draw(B--G--E);
(Error making remote request. Unknown error_msg)
Let 
, 
, 
, 
and 
. Then we know that 
=73, 
, 
, 
and 
. From this we can easily deduce 
and 
thus 
. Using Heron's formula we can calculate the area of 
to be 
, and since the base of 
is 
of that of , we calculate the area of to be 
.
See also
| 2025 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by First Problem |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
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