#Similarity

3 messages · Page 1 of 1 (latest)

vernal fjord
#

I have two intersecting lines and a point P on neither. I'm supposed to use similarity to show that a circle tangent to both lines and going through P can be constructed but I don't know where to start. Can anyone help point me in the right direction?

vernal fjord
#

I think I have a solution, actually. Just draw an arbitrary circle that is tangent to the lines, which let's say intersect at O. If we draw the line PO, that line will intersect our arbitrary circle at two points.

#

Say P'1 and P'2. We can construct two similar circles then by scaling our arbitrary circle that go through P. The ratios will be OP/OP'1 and OP/OP'2.