# BMO 2006/7 circles question

• Aug 2nd 2011, 04:17 AM
abhishekkgp
BMO 2006/7 circles question
Two touching circles S and T share a common tangent which meets
S at A and T at B. Let AP be a diameter of S and let the tangent
from P to T touch it at Q. Show that AP = PQ.

If you have solved it then please give me a hint(don't post the full solution).
• Aug 3rd 2011, 06:33 AM
earboth
Re: BMO 2006/7 circles question
Quote:

Originally Posted by abhishekkgp
Two touching circles S and T share a common tangent which meets
S at A and T at B. Let AP be a diameter of S and let the tangent
from P to T touch it at Q. Show that AP = PQ.

If you have solved it then please give me a hint(don't post the full solution).

1. Draw a sketch!

2. Prove(!) that the described situation is only possible if the 2 circles are congruent.

3. Prove that the 2 diameters and the tangent segments consequently form a square.
• Aug 3rd 2011, 08:03 AM
abhishekkgp
Re: BMO 2006/7 circles question
Quote:

Originally Posted by earboth
1. Draw a sketch!

2. Prove(!) that the described situation is only possible if the 2 circles are congruent.

3. Prove that the 2 diameters and the tangent segments consequently form a square.

I have attached a sketch. The two circle S and T drawn are not congruent but i still get AP=PQ.