Similar Triangles (Posted on 2013-11-15)

	Submitted by Bractals
Rating: 4.0000 (1 votes)
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Let the geometric points be represented by complex numbers.                                                    A-P          C-P    ΔPAB ~ ΔPCD (direct)  <==>  -------- = ---------                                                    B-P          D-P Solving for P gives                  BC - AD    P = ---------------------             (B+C) - (A+D) The denominator equals zero if and only if the midpoints of sides AD and BC coincide. Since ABCD is a simple quadrilateral, point P exists. WOLOG let A=0 and B=1, then    P = C/(C-D+1). Let F = C-D+1, then P = C/F. Construct the point F using vectors,    AF = AC - AD + AB. Construct point P by constructing ΔABP such that ΔABP ~ ΔAFC (Direct). QED

	Subject	Author	Date
	re(6): Argand - grand!	Harry	2013-12-04 14:09:41
	re(5): Argand - grand!	Bractals	2013-12-04 05:14:19
	re(4): Argand - grand!	Harry	2013-12-03 20:28:08
	re(3): Argand - grand!	Bractals	2013-12-03 17:39:31
	re(2): Argand - grand!	Harry	2013-12-03 12:47:12
	re: Argand - grand!	Bractals	2013-11-28 22:36:03
	Argand - grand!	Harry	2013-11-27 14:27:13
	re(2): Solution	Harry	2013-11-24 18:31:59
	re: Solution	Bractals	2013-11-24 14:59:58
	Solution	Harry	2013-11-23 20:44:38