1. V

    An intersection circle problem

    The circles k1 and k2 intersect at points A and B. The common tangent touches them at points M and N. Calculate the sum of the convex angles ∠ MAN and ∠ MBN.
  2. Chemist116

    How to obtain the resultant and its modulus from a group of vectors in a circle?

    The problem is as follows: Find the modulus of the resultant from the vectors shown in the picture from below: The alternatives given on my book are: $\begin{array}{ll} 1.&10\,\textrm{inch}\\ 2.&20\,\textrm{inch}\\ 3.&10\sqrt{3}\,\textrm{inch}\\ 4.&20\sqrt{3}\,\textrm{inch}\\...
  3. Chemist116

    How can I find the resultant and norm from pair of vectors passing in half a circle?

    I've been walking in circles (no pun intended) with this problem. It states as follows: A certain sugar is analyzed at an optical laboratory. The tecnician passes two beams in the visible spectra one orange and the other lightblue. These describe the vectors labeled A and B (see the figure...
  4. G

    Prove that these 3 points are in the same half circle.

    Prove that A(-10;-12) B(6;8) C(-2;-14) are in the same half circle. Please help; been torturing myself all morning.
  5. E

    Slope of the Unit Circle at Any Point

    How do you calculate the slope of the unit circle at any point? Unlike curves that can be written in the form y = ax^2 + bx + c, which are easy to take the derivative of, writing the unit circle in y = form would have a positive or negative in front of a square root.
  6. N

    3 circle Venn

    sir/miss would you please help me out. I am okay with written English but having problems linking and turning them into mathematical concepts. can anyone teach me how to approach this the easy way for junior level like me. Many thanks.
  7. V

    Height of a Circle's segment

    Given the chord length and area of a segment of circle, how can we find the height of the segment?
  8. Z

    Please explain to me in simple terms what these circle intersections are all about.

    So, say you got 4 circles intersecting this way: Now, I am looking for two things: A proof that each part of the circle which is in an intersection is 1/4 the size of the whole circle's circumference The exact area of the non-shaded region. Now, in my search for finding the answer to...
  9. S

    The Excel Circle Challenge

    The following formula solution request will be used within a High School students Math class challenge problem. The general problem is to create one formula that combines the Unit-Circle (radius = 1) equation (x^2+y^2 = 1) and the Slope Intercept equation for a line segment (y = mx+b)...
  10. K

    Circle Trigonometry

    The area of a circle is 15 cm^2 and the length of its arc is 3 cm. Calculate the radius of the sector and its angle. May somebody help please
  11. N

    Circle and triangle

    A circle k(O) with diameter AB is given. Lines PC and PD touch k (C, D \in k). AC \cap BD = K. Show that PK \bot AB. I have tried to calculate some angles if \angle DCP = \angle PDC = \alpha but it seems useless at the end. I also see that \angle ACB = \angle ADB = \frac...
  12. A

    Circle Proof Help

    In the diagram below, quadrilateral ABCD is inscribed in circle O. AB is parallel to DC, and diagonals AC and BD are drawn. Prove that triangle ACD is congruent to BDC. I have listed the givens and stated that DC is congruent to DC because of the reflexive property, but I’m stuck after this.
  13. P

    Set operations. Various Set operations like Union, Intersection, Complement, Cartesian product etc are shown with Circle as Geometrical figure. Other than Circle Geometrical shape, Which could be other Geometrical shapes where these operations can be...
  14. R

    Problem involving a unit circle and two other coordinates

    I have a little problem that I hope the community would be able to assist me with. I have a unit circle and inside that unit circle I have a point (A), outside that unit circle I have another point (B). Is there a way to find the coordinates of the point that intersects the radius of the unit...
  15. T

    The Area of the region of the Equilateral Triangle that lies Outside the Circle

    I'm considering a circle of diameter D superimposed over the equilateral triangle of side length D, with their centres coinciding. What is the total area of the three regions of the triangle that lie outside the circle?
  16. L

    Rectangle inscribed in a circle

    Is the area of a rectangle inscribed in a circle ever rational?
  17. S

    Example of properties that the circle unit hasn't

    What are the properties the unit circle hasn't, but that ellipses have?
  18. A

    Diameter of a circle

    The inverse of one angle and the side opposite to the angle, which is equal to one, in all triangles gives a diameter of the circumscribed circle. In a right triangle, the inverse of the angle is always 1, which is the circle's diameter, and its opposite's side is 1, that is hypotenuse of 1...
  19. O

    circle squared

    Who constructed nearest approximation of squaring circle and what geometrical method had been used (only with compass and straightedge)?
  20. D

    Circumference of smaller half circle removed inside of half circle?

    So I was trying to find the circumference of a half circle inside of a half circle. By that I mean that I have an empty half circle inside of the larger half circle. So I will need to subtract the smaller half circle at the end. Circumference of half circle: (\pi * d) / 2 So assuming what...