Angle Chasing
Let the two base angles of triangle ABC be A = 10 and B = 20. The altitude to the base from angle C divides the vertex angle C into two parts, C1 and C2, with C1 > C2. Find C1 - C2.
10
In Triangle ABC, M and N are the midpoints of AB and AC respectively. If AB = 5, BC = 6 and AC = 7, find MN.
3
How many points with integer coordinates are exactly 5 units away from (0, 0)?
12
An equilateral triangle and a regular hexagon have equal perimeters. If the area of the triangle is 2, find the area of the hexagon.
3
Which university did Varin Dharia commit to?
Rutgers
In Triangle ABC, D is a point on side AC such that BD=DC and Angle BCD measures 70 degrees. What is the degree measure of Angle ADB?
140
Triangle ABD is right-angled at B. On AD there is a point C for which AC = CD and AB = BC.
Find Angle DAB.
60
The graphs of the equations x + 3y = 6 and
kx + 2y = 12 are perpendicular. Find the value of k.
-6
If the sum of all the angles except one of a convex polygon is 2190 degrees, then how many sides does the polygon have?
15
The Math Team most recently won the School Merit Award in 2023. What was the first year the School Merit Award won?
2008
We are given points A, B, C, and D in the plane such that AD = 13 while AB = BC = AC = CD = 10. Find Angle ADB.
30
In Triangle ABC, a point E is on AB with AE = 1 and EB=2. Point D is on AC so that DE || BC and point F is on BC so that EF || AC. What is the ratio of the area of CDEF to the area of Triangle ABC?
4/9
A triangle has vertices with coordinates A(0, 15), B(0,0), and C(10, 0). Find the coordinates of point D on AC so that the area of triangle ABD is equal to the area of triangle DBC.
(5, 7.5)
In regular polygon ABCDE..., we have Angle ACD = 120 degrees. How many sides does the polygon have?
9
Who were the Co-Presidents Prior to Aaron Wong's presidency?
Austin Yang and Varin Dharia
Let ABC be a traingle with angle BAC = 117. The angle bisector of angle ABC intersects side AC at D. Suppose triangle ABD and triangle ACB are similar. Compute the measure of angle ABC in degrees. (Recall similarity statement pair vertices together and "similar" vertices have the same angle)
42
The base of a triangle is 15 inches. Two lines are drawn parallel to the base, terminating in the other two sides and dividing the triangle into three equal areas. What is the length of the parallel closer to the base?
5sqrt6
Rectangle ABCD has AB = 5 and BC = 4. Point E lies on AB so that EB = 1, point G lies on BC so that CG = 1, and point F lies on CD so that DF = 2. Segments AG and AC intersect EF at Q and P, respectively. What is the value of PQ / EF?
10/91
Find the area of a regular dodecagon (12-sided shape) if its circumscribed circle has a circumference of 12pi.
108
What was the record number of AIME qualifiers up to the year 2008? (Hint; Ms. Berkovich led this team)
29
Triangle ABC has AB=2AC. Let D and E be on AB and BC, respectively, such that Angle BAE = Angle ACD. Let F be the intersection of segments AE and CD, and suppose that Triangle CFE is equilateral. What is Angle ACB?
90
Right triangles T1 and T2, have areas of 1 and 2, respectively. A side of T1 is congruent to a side of T2, and a different side of T1 is congruent to a different side of T2. What is the square of the product of the lengths of the other (third) sides of T1 and T2?
28/3
A square in the coordinate plane has vertices whose y-coordinates are 0, 1, 4, and 5. What is the area of the square?
17
In a 5 by 12 rectangle, one of the diagonals is drawn and then circles are inscribed in both right triangles formed. Find the distance between the centers of the two circles.
sqrt65
Who is the only person to have participated on an East Brunswick HMMT Team yet was not a member of the EBHS Math Team? (Hint; he's asian)
Jason Li