Show that 3 points are aligned

[Alassane]

These are two secants circles in A and B such as the radii [OA] and [O'A] are perpendicular. M belongs to one circle and C and D are repectively the intersections of (MA) and (MB) with the other circle
Show that C, D and O' are aligned.

 

[Deleted member 4993]

View attachment 30412

These are two secants circles in A and B such as the radii [OA] and [O'A] are perpendicular. M belongs to one circle and C and D are repectively the intersections of (MA) and (MB) with the other circle
Show that C, D and O' are aligned.

What are the different ways you can show that three points are collinear ?

 

[Steven G]

If you want help from helpers from this forum that is great. However you need to follow the posting guidelines. Have you read them?

 

[Alekos]

Fo DO'C to be a straight line you need to show that MDC is a triangle i.e the angles must sum to 180 deg. Start from there.
Also, the important identity in this scenario is that the line between the intersection points AB is a perpendicular bisector to the line between the centres OO'

 

[Dr.Peterson]

Fo DO'C to be a straight line you need to show that MDC is a triangle i.e the angles must sum to 180 deg. Start from there.
Also, the important identity in this scenario is that the line between the intersection points AB is a perpendicular bisector to the line between the centres OO'

No.

MDC is a triangle regardless, because it has three vertices. You must mean something other than what you said, probably something involving O'.

And although OO' is a perpendicular bisector of AB, AB is not a perpendicular bisector of OO'.

I'd be looking at triangle ACD. Try marking up angles to find angle MAD.

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