MathDB

3

Part of 2023 AIME

Problems(2)

Intersecting Lines in a Plane

Source: 2023 AIME I #3

2/8/2023
A plane contains 4040 lines, no 22 of which are parallel. Suppose there are 33 points where exactly 33 lines intersect, 44 points where exactly 44 lines intersect, 55 points where exactly 55 lines intersect, 66 points where exactly 66 lines intersect, and no points where more than 66 lines intersect. Find the number of points where exactly 22 lines intersect.
AMCAIMEAIME I
similar triangles yay

Source: 2023 AIME II Problem #3

2/16/2023
Let △ABC\triangle{ABC} be an isoceles triangle with ∠A=90∘\angle A=90^{\circ}. There exists a point PP inside △ABC\triangle{ABC} such that ∠PAB=∠PBC=∠PCA\angle PAB=\angle PBC=\angle PCA and AP=10AP=10. Find the area of △ABC\triangle{ABC}.
geometryAIMEAIME II