Knights

1. Analytic Geometry - lengths?

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 radius 4 and center A at points P and D . What is the distance from P to AD? Please help - I drew the diagram, but looks kinda
2. Trigonometry - Cosine of angle

What is the cosine of the angle between two adjacent faces of a regular tetrahedron? (We define the angle between two intersecting planes as the angle between two intersecting lines, one in each plane, such that each line is perpendicular to the line at
3. Triangle inequality?

Two altitudes of a triangle have lengths 12 and 14. What is the longest possible length of the third altitude, if it is a positive integer? I tried using the triangle inequality but to no avail...how would I do this?
4. Analytic Geometry - Circles and Areas

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 R4. Let [Ri] denote the area of region Ri. If [R1]>[R2]>[R3]>[R4] , then compute [R1]-[R2]-[R3]+[R4]. Could someone help me, I
5. Circumcenter of Triangle in circle

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 circumcenter of BCO in its interior. If the area of circle with center O is 48pi, then what is the area of triangle ABC? How to do
6. Trigonometry question?

Let ABCD be a square, and let M and N be the midpoints of BC and CD respectively. Find sin
7. Centroids and Triangles - determining perimeter?

Let G denote the centroid of triangle ABC. If triangle ABG is equilateral with side length 2, then determine the perimeter of triangle ABC. I drew the diagram, but it doesn't really help....
8. Bisectors in a Triangle

Let ABC have side lengths AB=13, AC=14, and BC=15. There are two circles located inside
9. Circles / Square

Alicia has a flat platter shaped like a square with a semicircle of diameter 10 inches on each edge. What is the number of inches in the side length of the smallest square that can contain the platter (which contains the square with the semicircles on each

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 tangent to the smaller circle, and crosses the goes through the larger circle and hits the other side at D. TD is a diameter,
11. Circle Geometry - chords in a circle

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 RS and TU is also 4. If PQ = 78 TU=50 , then find RS. how to do this? Draw some lines?
12. Geometry - Circles and tangents

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 to the circle with diameter QR , and from R a parallel tangent is drawn to the circle with diameter PQ . Find the distance
13. Geometry - semicircle inside isosceles triangle

Isosceles triangle ABC has sides of length AB=AC=25 and BC=40 . Find the area of a semicircle inscribed in triangle ABC with diameter along BC . Please help I do not know how to start....
14. analytic geometry/graphing problem

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 circle passing through all three vertices. I don't understand how to solve this: should I set them all equal to find the
15. Trigonometry - finding cos 36 given cos 72?

Please help, I know cos 72 degrees = (sqrt 5 - 1)/4. I need to know what cos 36 degrees is. How to do so?
16. slope and graphing

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 find the average? Do we build isosceles triangles?
17. Graphing Circles - Finding the radius

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 using distance formula but it doesnt work? Help please thanks.

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 this line? I tried putting one point where the line intersects the square as (y,1), and the other as (x,0), and the y intercept

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 am i supposed to figure this out??
20. Analytic geometry - finding point by intersect lin

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 lines: Altitude from A to BC, altitude from B to AC, and altitude from C to AB. I know their slope because it is just
21. Analytic Geometry - Reflecting points over lines

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 start? Should we draw perpendicular lines? Analytic Geometry - Reflecting points over lines - Steve, Monday, March 4, 2013 at
22. Analytic Geometry - Reflecting points over lines

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 start? Should we draw perpendicular lines?
23. Geometry - Dilation of a square

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 horizontal. The square is then dilated with the dilation center at (0,0) and a scale factor of 2. What are the coordinates of the vertex
24. analytic geometry helps are appreciated

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 begin? As a matter of fact, how is there not only like 1 solution??
25. analytic geometry helps are appreciated

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 begin? As a matter of fact, how is there not only like 1 solution?? No one has answered this question yet.

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 begin? As a matter of fact, how is there not only like 1 solution??
27. analytic geometry helps are appreciated

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 equations together??
28. analytic geometry helps are appreciated

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. How is this even going to be done? We are given little info but a bunch of variables. Could someone help please??

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?
30. Help please with reflection problem!?

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 the sides of the square, until it hits another vertex, at which point it stops. What is the length of the path the laser takes?

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 the sides of the square, until it hits another vertex, at which point it stops. What is the length of the path the laser takes?

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 k. I do not understand...it is not 3/2, as I was told, but I don't understand why? Help?
33. Geometry - Transformations and Dilations

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 k. I do not understand...it is not 3/2, as I was told, but I don't understand why? Help?

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 diagram, calling the trapezoid ABCD with A and D at the bottom, I see that the length from where the altitude from B and C hits
35. I need help on a geometry cone/frustrum problem

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 of the frustum.) Find the volume of the frustum. Could someone help me? I can't find the radius of the cone....
36. Mathematics -- Geometry --

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 holes are drilled in the ball. Bowler Kris has holes drilled that are 8 cm deep and have diameters of 2 cm, 2 cm, and 3 cm.

PLEASE HELP I REALLY NEED HELP. Each of the three circles in the figure below is externally tangent to the other two, and each side of the triangle is tangent to two of the circles. If each circle has radius three, then find the perimeter of the triangle.

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 = PC^2 + PD^2 It can be solved using geometry methods (no trig). Anyway, I figured out that PA^2 +PB^2 = 2OP^2 + 2OB^2. However,
39. Mock Trial

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 learn from it? Thanks all and Happy New Year!
40. triangle inequality - altitudes help plz

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 have lengths 12 and 14. What is the longest possible length of the third altitude, if it is a positive integer? Thanks in advance
41. altitude triangle inequality

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 have lengths 12 and 14. What is the longest possible length of the third altitude, if it is a positive integer? Thanks in advance
42. geometry inequality triangles help if you can

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 integer? i know that in an obtuse triangle a^2+b^2c but i tried plugging in and it wont work so couldyou guys help me? btw merry
43. math problem triangle inequality help

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 tried listing them all but I get confused...Please help thank you!
44. Help triangle angles!

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
45. double square root problem?

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 root so what then? how to simplify?
46. help hexagon geometry

A regular hexagon is inscribed in a circle and another regular hexagon is circumscribed about the same circle. What is the ratio of the area of the larger hexagon to the area of the smaller hexagon? Express your answer as a common fraction. How is this

The distance between two opposite vertices of the dodecagon is 2. Find the area of the dodecagon. first, what is the area of a dodecagon and second how to find it with just the distance between two oppositve vertices. i found that a dodecagon can be
48. A probability question i think

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 right. How many ways are there for a lord to move from the bottom left to top right corner of the 8 by 8 chessboard? Thanks in