Hence if a chord is a focal chord then the tangents drawn from the endpoints of this focal chord intersect at right angles on the directrix. Example 9 (Reflection Property) Prove that a ray of light parallel to the axis entering a parabolic mirror passes through the focus after reflection from the mirror.
For the mathematics for the intersection point(s) of a line (or line segment) and a sphere see this. Antipodal points. A line that passes through the center of a sphere has two intersection points, these are called antipodal points. Planes through a sphere. A plane can intersect a sphere at one point in which case it is called a tangent plane.
(i) As the two chords AB and CD intersect each other at P, we have AP x PB = CP x PD 4.5 x PB = 3 x 9 [3CP = 9 cm so, CP = 3 cm] PB = (3 x 9)/ 4.5 = 6 cm
Let the point of tangency of the chord on the little circle be A A A, and an endpoint of the chord be B B B. Finally, let the radius of the small circle be r r r and the radius of the large circle be R R R. Notice that A B = 4 AB=4 A B = 4, because A B AB A B is half of the chord, which has length 8 8 8.
Algebra Calculator is a calculator that gives step-by-step help on algebra problems. See More Examples » x+3=5. 1/3 + 1/4. y=x^2+1. Disclaimer: This calculator is ...
Intersect Menu. 9.06 Bearing-Distance Intersection (BD). FUNCTION: The Bearing-Distance Intersection routine is used to calculate the coordinates of a point generated by the intersection of a line of known bearing with a line of known distance.
Aug 07, 2015 · I am trying to come up with an excel spreadsheet that will calculate the 2 intersection points of 2 intersecting circles. Input is X any Y center points of the 2 circles and radii of the 2 circles. Output would be the 2 X and Y intersecting coordinates at their intersection.
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Dec 03, 2020 · Understand a definition of Euclid's Intersecting Chords Theorem. The Intersecting Chords Theorem asserts the following very useful fact: Given a point P in the interior of a circle with two lines passing through P, AD and BC, then AP*PD = BP*PC -- the two rectangles formed by the adjoining segments are, in fact, equal.