Tangent

Radius of Circle of New Atom Smasher

Problem
A new kind of atom smasher is to be composed of two tangents and a circular arc which is concave toward the point of intersection of the two tangents. Each tangent and the arc of the circle is 1 mile long, what is the radius of the circle? Use 1 mile = 5280 ft.

A.   1437 ft. C.   1347 ft.
B.   1734 ft. D.   1374 ft.

 

Equation of a curve with given equation of slope and passing through a point

Problem
What is the equation of the curve passing through the point (3, -2) and having a slope at any point (x, y) equal to (x2 + y2) / (y3 - 2xy)?
 

Relationship Between Central Angle and Inscribed Angle

Central angle = Angle subtended by an arc of the circle from the center of the circle.
Inscribed angle = Angle subtended by an arc of the circle from any point on the circumference of the circle. Also called circumferential angle and peripheral angle.
 

Figure below shows a central angle and inscribed angle intercepting the same arc AB. The relationship between the two is given by
 

$\alpha = 2\theta \, \text{ or } \, \theta = \frac{1}{2}\alpha$

 

if and only if both angles intercepted the same arc. In the figure below, θ and α intercepted the same arc AB.
 

The Circle

The following are short descriptions of the circle shown below.

Tangent - is a line that would pass through one point on the circle.
Secant - is a line that would pass through two points on the circle.
Chord - is a secant that would terminate on the circle itself.
Diameter, d - is a chord that passes through the center of the circle.
Radius, r - is one-half of the diameter.

 

Subscribe to RSS - Tangent