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Knights

Questions (52)

Square ABCD has sides of length 4, and M is the midpoint of CD . A circle with radius 2 and center intersects a circle with
1. 1 answer
2. 1,543 views
What is the cosine of the angle between two adjacent faces of a regular tetrahedron? (We define the angle between two
1. 2 answers
2. 651 views
Two altitudes of a triangle have lengths 12 and 14. What is the longest possible length of the third altitude, if it is a
1. 2 answers
2. 751 views
Let R denote the circular region bounded by x^2+y^2 = 36. The lines x=4 and y=3 partition R into four regions R1, R2 ,R3 , and
1. 2 answers
2. 1,426 views
Equilateral triangle ABC and a circle with center O are constructed such that BC is a chord of the circle and point A is the
1. 0 answers
2. 720 views
Let ABCD be a square, and let M and N be the midpoints of BC and CD respectively. Find sin<MAN.
1. 10 answers
2. 7,911 views
Let G denote the centroid of triangle ABC. If triangle ABG is equilateral with side length 2, then determine the perimeter of
1. 9 answers
2. 2,854 views
Let ABC have side lengths AB=13, AC=14, and BC=15. There are two circles located inside <BAC which are tangent to rays AB, AC ,
1. 1 answer
2. 2,764 views
Alicia has a flat platter shaped like a square with a semicircle of diameter 10 inches on each edge. What is the number of
1. 11 answers
2. 3,288 views
Two circles of different sizes are tangent at T. A is on the smaller circle, whereas B is on the larger one. Also, segment CD is
1. 0 answers
2. 651 views
Let PQ, RS , and TU be parallel chords of a circle. The distance between chords PQ and RS is 4, and the distance between chords
1. 8 answers
2. 1,826 views
Two circles of radius 1 are externally tangent at Q . Let PQ and QR be diameters of the two circles. From P a tangent is drawn
1. 2 answers
2. 2,349 views
Isosceles triangle ABC has sides of length AB=AC=25 and BC=40 . Find the area of a semicircle inscribed in triangle ABC with
1. 12 answers
2. 2,751 views
The vertices of a triangle are the points of intersection of the line y=-x-1, x=2 and y = 1/5x + 13/5. Find an equation of the
1. 2 answers
2. 1,376 views
Please help, I know cos 72 degrees = (sqrt 5 - 1)/4.I need to know what cos 36 degrees is. How to do so?
1. 2 answers
2. 615 views
The lines y=5/12x and y=4/3 are drawn in the coordinate plane. Find the slope of the line that bisects these lines.How? Do we
1. 1 answer
2. 500 views
A circle is tangent to the y-axis at the point (0,2) and passes through the point (8,0). Find the radius of the circle.I tried
1. 2 answers
2. 1,083 views
A line with slope 6 bisects the area of a unit square with vertices (1,0), (0,0) , (1,1), and (0,1). What is the y-intercept of
1. 3 answers
2. 917 views
Find the largest real number x for which there exists a real number y such that x^2+y^2 = 2x+2y .I think it is a circle, but how
1. 3 answers
2. 688 views
I have a triangle ABC. The slope of AB is -1/ab, the slope of AC is -1/ac, and the slope of BC is -1/ac. My question is, I have
1. 2 answers
2. 585 views
Let P = (5,1), and let Q be the reflection of P over the line y = 1/2x + 2. Find the coordinates of Q.I don't understand how to
1. 6 answers
2. 1,713 views
Let P = (5,1), and let Q be the reflection of P over the line y = 1/2x + 2. Find the coordinates of Q.I don't understand how to
1. 2 answers
2. 605 views
The preimage of square ABCD has its center at (8,-8) and has an area of 4 square units. The top side of the square is
1. 1 answer
2. 1,550 views
Find the maximum value of y/x over all real numbers x and y that satisfy (x-3)^2+(y-3)^2 = 6.It is a circle, but how do we even
1. 2 answers
2. 581 views
Find the maximum value of y/x over all real numbers x and y that satisfy (x-3)^2+(y-3)^2 = 6.It is a circle, but how do we even
1. 0 answers
2. 457 views
Find the maximum value of y/x over all real numbers x and y that satisfy (x-3)^2+(y-3)^2 = 6.It is a circle, but how do we even
1. 2 answers
2. 946 views
For some positive real number r , the line x+y=r is tangent to the circle x^2+y^2 = r. Find r.How do we do this? Set equal
1. 4 answers
2. 1,405 views
A line with slope 3 is 2 units away from the origin. Find the area of the triangle formed by this line and the coordinate axes.H
1. 4 answers
2. 2,394 views
What is the area, in square units, of a triangle whose vertices are at (4,-1), (10,3) and (4,5) ?How to do this?
1. 5 answers
2. 1,791 views
A laser is shot from vertex A of square ABCD of side length 1, towards point P on BC so that BP = 3/4. The laser reflects off
1. 5 answers
2. 3,699 views
A laser is shot from vertex A of square ABCD of side length 1, towards point P on BC so that BP = 3/4. The laser reflects off
1. 0 answers
2. 862 views
When a square of area 4 is dilated by a scale factor of k, we obtain a square of area 9. Find the sum of all possible values of
1. 5 answers
2. 2,694 views
When a square of area 4 is dilated by a scale factor of k, we obtain a square of area 9. Find the sum of all possible values of
1. 2 answers
2. 797 views
A circle with radius 3 is inscribed in a isosceles trapezoid with legs of 10. Find the length of the smaller base.When I draw a
1. 2 answers
2. 782 views
A sphere with radius 3 is inscribed in a conical frustum of slant height 10. (The sphere is tangent to both bases and the side
1. 4 answers
2. 1,912 views
A bowling ball is a solid ball with a spherical surface and diameter 30 cm. To custom fit a bowling ball for each bowler, three
1. 3 answers
2. 3,904 views
PLEASE HELP I REALLY NEED HELP.Each of the three circles in the figure below is externally tangent to the other two, and each
1. 3 answers
2. 1,477 views
Let AB be the diameter of a circle, and let point P be a point on AB. Let CD be a chord parallel to AB. Prove that PA^2 + PB^2 =
1. 0 answers
2. 1,150 views
Hi all,I belong to a education group, and we practice Mock Trial. Where can I find a video of a real trial going on so I can
1. 1 answer
2. 515 views
hi guys ive be struggling on this problem for a couple of days, so please help if you canProblem:Two altitudes of a triangle
1. 4 answers
2. 782 views
hi guys ive be struggling on this problem for a couple of days, so please help if you canProblem:Two altitudes of a triangle
1. 1 answer
2. 600 views
Two sides of an obtuse triangle are 16 and 21. How many possible lengths are there for the third side, if it is a positive
1. 7 answers
2. 3,558 views
Two sides of a triangle are 11 and 17. How many possible lengths are there for the third side, if it is a positive integer?I
1. 5 answers
2. 3,551 views
Points D, E, and F are the midpoints of sides BC, CA, and AB of ABC, respectively, and CZ is an altitude of the triangle. If
1. 2 answers
2. 1,041 views
Hi I do not how to simplify the problemx^2 =40+12sqrt2 what would be x? BTW if you sqrt both sides it would be double square
1. 1 answer
2. 612 views
A regular hexagon is inscribed in a circle and another regular hexagon is circumscribed about the same circle. What is the ratio
1. 7 answers
2. 7,863 views
The distance between two opposite vertices of the dodecagon is 2. Find the area of the dodecagon.first, what is the area of a
1. 2 answers
2. 911 views
In a chess variant, a "lord" can move one space at a time, either upward, or to the right, or diagonally upward and to the
1. 17 answers
2. 4,677 views
An equilateral triangle of side 14 centimeters is revolved about an altitude to form a cone. What is the number of cubic
1. 6 answers
2. 2,439 views
Please help guys if you can, this is a really hard problem I am trying to solveFour circles of unit radius are drawn with
1. 2 answers
2. 727 views
The diagonals of a trapezoid are perpendicular and have lengths 8 and 10. Find the length of the median of the trapezoid.I tried
1. 2 answers
2. 1,050 views
The diagonals of a trapezoid are perpendicular and have lengths 8 and 10. Find the length of the median of the trapezoid.I don't
1. 7 answers
2. 1,589 views

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