Any four exterior vertices determine a cyclic quadrilateral, and all cyclic quadrilaterals are convex quadrilaterals, so each set of four exterior vertices have exactly one point of intersection formed by their diagonals ( chords ).

Any set of five points in the plane in general position has a subset of four points that form the vertices of a convex quadrilateral.

Any three of the lines of the quadrilateral form the sides of a triangle ; the orthocenters of the four triangles formed in this way lie on a second line, perpendicular to the one through the midpoints.

The construction requires a quadrilateral with sides 2a, b, 2c, b. Any side must be less than the sum of the remaining sides, so the curve is empty ( at least in the real plane ) unless a < b + c and c < b + a.

Any posse riding down the street to demand Blue Throat's surrender would be wiped out with one deadly burst of fire.

Any abilities I may have were achieved in their present shape from experience in sharing in the growth and control of my business, coupled with raising my family.

Any attempt to reconcile this statement of the central issue in the campaign of 1956 with the nature of the man who could not conceive it as the central issue will at least resolve our confusions about the chaotic and misleading results of the earnestness of both doctors and President in a situation which should never have arisen.

Any claimant whose claim is denied, or is approved for less than the full amount of such claim, shall be entitled, under such regulations as the Commission may prescribe, to a hearing before the Commission, or its duly authorized representatives, with respect to such claim.

Any irregularity on the piston heads will make it impossible, with normal means, to determine the final combustion chamber volume because the volume displaced by the piston heads cannot be readily computed.

Any reputable French interne can supply you with a dozen similar instances, and I'll presently recount a case out of my own personal experience, but, for the moment, let's resume our catalogue.

Any of the antithyroid drugs, of either type, if given in large enough doses for a long period of time will cause goitre, owing to inhibition of thyroid hormone synthesis, with production of hypothyroidism.

Any adjustments which are made, Mr. Grenier said earlier this month, will appear on the balance of the tax bill since most of the town's taxpayers take the option of paying quarterly with the balance due next year.

Any shareholder of any of these funds who finds a mistake in his account certainly should get in touch with the bank.

Any musician playing Beethoven here, where Beethoven was born, is likely to examine his own interpretations with special care.

* Any ring of matrices with coefficients in a commutative ring R forms an R-algebra under matrix addition and multiplication.

Most of the C code being written nowadays is based on ANSI C. Any program written only in standard C and without any hardware dependent assumptions is virtually guaranteed to compile correctly on any platform with a conforming C implementation.

Any company incorporating Bluetooth wireless technology into products, using the technology to offer goods and services or simply re-branding a product with Bluetooth technology must become a member of the Bluetooth SIG.

Any codex of Bede's Easter cycle is normally found together with a codex of his " De Temporum Ratione ".

Love and Erlandson continued to pursue with the band, and released the single " Be A Man "— an outtake from the Celebrity Skin sessions — for the soundtrack of the Oliver Stone film Any Given Sunday ( 1999 ).

Any differential area with normal vector of a given internal surface area, bounding a portion of the body, experiences a contact force arising from the contact between both portions of the body on each side of, and it is given by

# Any collection of closed subsets of X with the finite intersection property has nonempty intersection.

Any season ticket holder could put themselves forward for election, with a certain number of nominations, and votes were cast by all season ticket holders over the age of 18.

Any pellets which are too small to be finished granules of couscous and fall through the sieve will be again rolled and sprinkled with dry semolina and rolled into pellets.

Any successes that the Nationalists did make, however, were met with constant political and military upheavals.

Any piece of DNA with the point centromere DNA sequence on it will typically form a centomere if present in the appropriate species.

# Any experience which is inconsistent with the organization of the structure of the self may be perceived as a threat, and the more of these perceptions there are, the more rigidly the self structure is organized to maintain itself.

Any rational number with a denominator whose only prime factors are 2 and / or 5 may be precisely expressed as a decimal fraction and has a finite decimal expansion.

Any units of angular measure can be used for declination, but it is customarily measured in the degrees ( ° ), minutes ( ' ), and seconds ( " ) of sexagesimal measure, with 90 ° equivalent to circle.

Any ellipse can be obtained by rotation and translation of a canonical ellipse with the proper semi-diameters.

Any word or phrase that exactly reproduces the letters in another order is an anagram.

:* Any total order on X has exactly one equivalence class, X itself, because x ~ y for all x and y ;

Any parabola can be repositioned and rescaled to fit exactly on any other parabola — that is, all parabolas are similar.

Any rule described here is simply a standard, and may or may not correspond exactly with any given promotion's ruleset.

# Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

Any version of Snakes and Ladders can be represented exactly as an absorbing Markov chain, since from any square the odds of moving to any other square are fixed and independent of any previous game history.

Any black box containing only voltage sources, current sources, and other resistors can be converted to a Norton equivalent circuit, comprising exactly one ideal current source and one resistor.

Any Black box ( systems ) | black box containing only voltage sources, current sources, and other resistors can be converted to a Thévenin equivalent circuit, comprising exactly one voltage source and one resistor.

** " Common variation ": Any player whose score hits exactly " 45 " is set back to Zero — The dreaded Forty-Five Rule.

Any mobile stack of height n ( with n > 0 ) can be moved ( in a straight line ) in any one of the 6 directions by exactly n spaces by the player controlling it, if it lands on another stack.

Any two closed curves in space, if allowed to pass through themselves but not each other, can be moved into exactly one of the following standard positions.

Any working theory must make Baum wrong about something, but fans may never reach a consensus on exactly what he was wrong about.

Any linear system containing only voltage sources, current sources, and other resistors can be converted to a Thévenin equivalent circuit, comprising exactly one voltage source and one resistor representing " internal resistance ".

( Any possible choice of parts will yield a valid interaction picture ; but in order for the interaction picture to be useful in simplifying the analysis of a problem, the parts will typically be chosen so that is well understood and exactly solvable, and contains some harder-to-analyze perturbation to this system.

Any abelian von Neumann algebra of operators on a separable Hilbert space is *- isomorphic to exactly one of the following

Any point in the space can then be identified to lie in exactly one of the regions.

Any three skew lines in R < sup > 3 </ sup > lie on exactly one ruled surface of one of these types.

Any exogenous changes affecting the IS curve ( such as government spending changes ) will be exactly offset by resulting exchange rate changes, and the IS curve will end up in its original position, still intersecting the LM and BoP curves at their intersection point.