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Knights
Questions and answers by
Knights
Questions (52)
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
6 answers
2,222 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
6 answers
1,225 views
A regular hexagon is inscribed in a circle and another regular hexagon is circumscribed about the same circle. What is the ratio
7 answers
asked by
Knights
7,609 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
5 answers
3,708 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
7 answers
3,456 views
Let ABCD be a square, and let M and N be the midpoints of BC and CD respectively. Find sin<MAN.
10 answers
7,750 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
7 answers
1,444 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
3 answers
943 views
Please help guys if you can, this is a really hard problem I am trying to solve
Four circles of unit radius are drawn with
3 answers
593 views
An equilateral triangle of side 14 centimeters is revolved about an altitude to form a cone. What is the number of cubic
7 answers
2,315 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
17 answers
4,481 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
3 answers
801 views
Hi I do not how to simplify the problem
x^2 =40+12sqrt2 what would be x? BTW if you sqrt both sides it would be double square
2 answers
508 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
3 answers
910 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
7 answers
3,443 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
7 answers
3,430 views
hi guys ive be struggling on this problem for a couple of days, so please help if you can
Problem:Two altitudes of a triangle
2 answers
507 views
hi guys ive be struggling on this problem for a couple of days, so please help if you can
Problem:Two altitudes of a triangle
5 answers
667 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 answer
419 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 answer
1,057 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
4 answers
1,313 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
5 answers
1,808 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
3 answers
645 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
3 answers
685 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
7 answers
2,522 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 answer
748 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?
6 answers
1,662 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
3 answers
804 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 answer
361 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
3 answers
487 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
3 answers
1,405 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
3 answers
496 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
7 answers
1,572 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
3 answers
454 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
4 answers
540 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
4 answers
766 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
3 answers
988 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 answer
427 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?
3 answers
538 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
3 answers
1,243 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
12 answers
2,580 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
4 answers
2,219 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
9 answers
1,676 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 answer
529 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
11 answers
3,125 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 ,
4 answers
2,595 views
Let G denote the centroid of triangle ABC. If triangle ABG is equilateral with side length 2, then determine the perimeter of
10 answers
2,719 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
3 answers
616 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
4 answers
1,287 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
3 answers
657 views
What is the cosine of the angle between two adjacent faces of a regular tetrahedron? (We define the angle between two
3 answers
537 views
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
3 answers
1,402 views