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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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jlacosta
Apr 2, 2025
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Geometry
AlexCenteno2007   3
N 2 hours ago by vanstraelen
Let ABC be an isosceles triangle with AB = AC and M the midpoint of BC. Consider a point E outside the triangle such that BE = BM and CE perpendicular to AB. The point of intersection of the perpendicular bisector of segment EB with the circumcircle of triangle AMB, which is on the same side as A with respect to BE, is point F. Show that angle FME = 90°
3 replies
AlexCenteno2007
Today at 3:49 AM
vanstraelen
2 hours ago
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Geometry
AlexCenteno2007   0
4 hours ago
Let A, B, C, and D be four distinct points on a straight line, in that order. The circles with diameters AC and BD intersect at X and Y. The straight line XY intersects BC at Z. Let P be a point on XY distinct from Z. The straight line CP intersects the circle with diameter AC at C and M, and the straight line BP intersects the circle with diameter BD at B and N. Show that AM, DN, and XY are aligned.
0 replies
AlexCenteno2007
4 hours ago
0 replies
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Geometry
AlexCenteno2007   2
N 4 hours ago by AlexCenteno2007
Let C be a point on a semicircle of diameter AB and let D be the mid-length of arc AC. Let E be the projection of point D on BC and F the intersection of AE with the semicircle. Prove that BF bisects segment DE.
2 replies
AlexCenteno2007
Today at 3:54 AM
AlexCenteno2007
4 hours ago
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(IDP),(O),(QEF) have a common point
kyotaro   0
5 hours ago
Given a non-isosceles triangle ABC inscribed in circle $(O)$. $X, Y, Z$ are the midpoints of $BC, CA, AB$ respectively. $P$ is the midpoint of arc $BAC$, $Q$ is symmetric to $P$ through $O$. Let $I, D, E, F$ be the incenter and tangent of angles $X, Y, Z$ of triangle $XYZ$ respectively. Prove that $(IDP),(O),(QEF)$ have a common point
0 replies
kyotaro
5 hours ago
0 replies
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ratio of volumes, pyramid with base trapezoid (2011 Euler Teachers' MO II p3)
parmenides51   0
Jul 13, 2020
The base of the $PABCD$ pyramid is the trapezoid $ABCD$, whose base $AD$ is twice the base BC. Line $MN$ os the midline of the triangle $ABP$ parallel to side $AB$. Find the ratio of the volumes of solids on which the plane $DMN$ divides the given pyramid.
0 replies
parmenides51
Jul 13, 2020
0 replies
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ratio of volumes, pyramid with base trapezoid (2011 Euler Teachers' MO II p3)
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parmenides51
#1 h  Jul 13, 2020, 6:19 AM
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The base of the $PABCD$ pyramid is the trapezoid $ABCD$, whose base $AD$ is twice the base BC. Line $MN$ os the midline of the triangle $ABP$ parallel to side $AB$. Find the ratio of the volumes of solids on which the plane $DMN$ divides the given pyramid.
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