Phuong Math
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- Jan 3, 2015
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Start with a circle with center at O and having radius of length R. Let BC be a chord of this circle (so B and C are on the circle), and let the length of BC be equal to the length of the radius R. Let A be a point on the major arc BC (being the arc which does not include the part of the circle cut off the by chord). In particular, note that A is not the same point as either B or C. Construct chords AB and AC.
Let M and N be points on the chord AC such that:
. . .\(\displaystyle \left|\, AC\, \right|\, =\, 2\, \left|\, AN\, \right|\, =\, \left(\dfrac{3}{2}\right)\, \left|\, AM\, \right| \)
Let P be a point on chord AB such that the segment MP is perpendicular to chord AB. Under the above conditions, prove that point P, center O, and point N are collinear.
Let M and N be points on the chord AC such that:
. . .\(\displaystyle \left|\, AC\, \right|\, =\, 2\, \left|\, AN\, \right|\, =\, \left(\dfrac{3}{2}\right)\, \left|\, AM\, \right| \)
Let P be a point on chord AB such that the segment MP is perpendicular to chord AB. Under the above conditions, prove that point P, center O, and point N are collinear.
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