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If the circumcenter of a triangle lies on a median of that triangle, the triangle is isosceles. Write the given and prove parts based on the diagram.
A rescue Helicopter at an altitude of 200 m spots two lost girls at the same time. Xavia is at an angle of depression of 13 degree.
Find the minimum and maximum limits for the length of the third side of a triangle if the other two sides and 83' and 117'.
Both ends of a rope of length 4.8m are attached to a horizontal beam, at points 4.2m apart. A chandelier hangs on the rope, 1.2m from one of its ends.
The coordinates of triangle a'b'c', the image of triangle abc after a reflection in the x-axis are a'------, ----- b'-----, ----- c'-----, -----?
Create two tangent circles with centers A and B. For convenience sake, let circle A have the larger radius.
Two distinct, nonparallel lines are tangent to a circle. See picture below. The measurement of the angle between the two lines is 54° (angle QVP).
In a circle of radius 6 centimeters, find the area of the segment bound by an arc of measure 120 degrees.
Two congruent semicircles lie on the diameter of a third semicircle, each tangent to the other two. A small circle is tangent to all three semicircles.
Two circles, A and B, touch each other at exactly one point, as shown in the diagram below. The equation of circle A is x2 - 18x + y2 - 2y + 46 = 0.
A circle of radius 100is inscribed in a square. The inscribing process continues to infinity. What is the sum of the unshaded areas?
Two cars with new tires are driven at an average speed of 60 mph for a test drive of 2000 miles. The diameter of the wheels of one car is 15 inches.
Given a circle, construct a circle with twice its area. I know that the r2 = (x-h)2 + (y+k)2 is the standard equation for a circle.
Further, we can specify that T take any 3 points on R onto any 3 points of R'. If we do specify Tz_j for j=2,3,4 (distinct z_j in R), then T is unique.
The sides of the triangle are on the lines 3x - y - 5 = 0, x + 3y - 1 = 0 and x - 3y + 7 = 0. Find the equation of the circle inscribed in the triangle.
The sleepers of a railway track which is turning round a bend of radius 60m are banked so that a train traveling at 40 km/hr .
A circle is the set of points that lie at a constant distance from one point, the center of the circle.
Using area integral in plane polar coordinates, calculate the total mass of the disc, in kg, when R=0.29m and k=25.02kgm^-2.
Find the points of intersection (if any) of the given pair of curves and draw the graphs.
For each of the following functions, find the maximum and mimimum values of the function on the circular disk.
Give an example of a non-rectifiable closed Jordan curve on the interval -1<=t<=1.
Find the area of the surface obtained when the graph of y=x^2 , 0<= x <= 1, is rotated around the y axis.
Compute the curvature k(t) of the curve r(t) = 2t i + 4sint j +4cost k
Formulate a linear optimization model to determine the optimal values of the parameters. Assume that the objective is to minimize the maximum.
Find the unit tangent and principle normal vectors at an arbitrary point h(s). Find the curvature k(s).