What is a Cross?

Geometry Level pending

Use the Cross Law from Rational Trigonometry to find cross of a set of three lines, non-concurrent, where the Quadrances (distance squared) related to the intersection of the three lines are equivalent.

Cross Law is ( Q 1 + Q 2 − Q 3 ) 2 = 4 Q 1 Q 2 c 3 (Q_1+Q_2-Q_3)^2=4Q_1Q_2c_3

Cross is c 3 = 1 − s 3 c_3=1-s_3 where s 3 s_3 is the spread formed by the lines.

− 1 4 \frac{-1}{4} − 3 4 \frac{-3}{4} 1 4 \frac{1}{4} 3 4 \frac{3}{4}

Peter Michael by Peter Michael , 37, Canada

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1 solution

Peter Michael
Jun 11, 2017

Q = Q 1 = Q 2 = Q 3 Q=Q_1=Q_2=Q_3

Q 2 = 4 Q 2 c 3 Q^2=4Q^2c_3

c 3 = 1 4 c_3=\frac{1}{4}

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