# Triangle inscribed in two circles...

• February 7th 2010, 02:19 PM
mdk
Triangle inscribed in two circles...
I need help with the set up of this problem...

Two circles meet at points P & Q. Let segment AP and segment BP be diameters of the circles. Show that segment AB passes through the other intersection Q. See attached file.

Any help would be greatly appreciated...
• February 7th 2010, 07:38 PM
pragraphic
Can we say angle PQA = angle PQB = 90 degree thus PQ perp AQB and so AQB is a line?
• February 8th 2010, 05:36 PM
mdk
Yes. That is what I thought later after working on it for a while. Thanks for the help.
• February 8th 2010, 09:10 PM
earboth
Quote:

Originally Posted by pragraphic
Can we say angle PQA = angle PQB = 90 degree thus PQ perp AQB and so AQB is a line?

Quote:

Originally Posted by mdk
Yes. That is what I thought later after working on it for a while. Thanks for the help.

If you add the radii in the 2 circles you get 2 isosceles triangles with the common base PQ. For symmetry reasons $PQ \perp CM$.

Since C respectively M bisect the diameters the triangles ABP is similar to triangle CMP. Thus you can show that AB is a straight line and that AB is twice as long as CM.