chapdawg147
New member
- Joined
- Nov 22, 2006
- Messages
- 6
The question is, If A, B, C, and D are four coplanar points with no three collinear, prove that circles ABC and ADC intersct at the same angle as the circles BDA and BCD.
So basically, there is a quadrilateral with a combinations of three point circles intersecting.
A property of inversions is that a directed angle of intersection of two circles* is unaltered in magnitude but reversed in sense by an inversion
*circles do not have to be circles, under inversion some circles become lines and some lines become circles
The books advice is to invert at one of the points. I guess I am just confused as to what the inverted quadrilateral will look like. Will it be that the s the circles will become straight lines making up a new quadrilateral where the points of intersection of the circles make up the points of the quadrilateral. I think I am on the right track I just can not figure out what the new quadrilateral look like. If any of you can help me out that would be wonderful.
So basically, there is a quadrilateral with a combinations of three point circles intersecting.
A property of inversions is that a directed angle of intersection of two circles* is unaltered in magnitude but reversed in sense by an inversion
*circles do not have to be circles, under inversion some circles become lines and some lines become circles
The books advice is to invert at one of the points. I guess I am just confused as to what the inverted quadrilateral will look like. Will it be that the s the circles will become straight lines making up a new quadrilateral where the points of intersection of the circles make up the points of the quadrilateral. I think I am on the right track I just can not figure out what the new quadrilateral look like. If any of you can help me out that would be wonderful.