Given two externally tangent circles with the tangency point P, draw two common secants AD and BC through P. Show that AB and CD are parallel.
My friend and I are really stuck on this, so if you could even give a few hints or somthing, it would be great!
2007-03-08 16:16:23 · 3 answers · asked by yogastar02 2 in Science & Mathematics ➔ Mathematics
Look, the secants AB and CD cross, forming the same angle on both sides of the intersection inside the circles. Draw a line through the centers of the circles and point P, so you can see how the circles and the lines inside them are similiar, even if scaled differently. Thus AB and CD are parallel. Rotate one of circles around 180 degrees about point P to understand what I'm talking about.
2007-03-08 16:27:44 · answer #1 · answered by Scythian1950 7 · 0⤊ 0⤋
Start by drawing out the problem. Draw 2 circles and have the tangency point be (0,0). Now draw 2 secant lines randomly. Label the 4 points of intersection. Now label the cordinates of each point. Meaning point A (-m,n) point D would be (m,-n), then B (-p,-q) point C would be (p,q). Now figure out the slopes (rise over run) of both AB and CD using the coordinates. If they are equal, then the lines are parallel.
2007-03-09 00:33:37 · answer #2 · answered by Brian K 2 · 0⤊ 1⤋
not sure sorry
2007-03-09 00:19:46 · answer #3 · answered by Anonymous · 0⤊ 3⤋